$\def\pm{{ ‰}} \def\pmf{{ ‰ \phantom.}} \def\pmm{{ ‰ \! ‰}} \def\pmmf{{ ‰ \! ‰ \phantom\%}} \DeclareMathOperator{\antilog}{antilog} \DeclareMathOperator{\arcsec}{arcsec} \DeclareMathOperator{\arccsc}{arccsc} \DeclareMathOperator{\arsinh}{arsinh} \DeclareMathOperator{\arcosh}{arcosh} \DeclareMathOperator{\arsech}{arsech} \DeclareMathOperator{\arcsch}{arcsch}$

## Integermania!

#### Four Fours

Four fours is a classic problem, dating back at least 90 years. Create each of the positive integers using four copies of 4, and any standard operations. All four numbers must be used, but no others. Your solutions will be assigned an exquisiteness level.

Use the online submissions page to get your Integermania solutions posted here!  This problem is now in semi-retired status, so you may submit an unlimited number of solutions each month.

Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-1600), Page 5 (1601-2000), Page 6 (2001-2400), Page 7 (2401+).

 1201 (3.6) $\dfrac{4!}{(\sqrt{4})\%} + \dfrac44$ Steve Wilson, 8/09Raytown, MO 1202 (3.8) $4! \times \dfrac{\sqrt{4}}{4\%} + \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1203 (4.0) $\dfrac{4! - (\sqrt{4})\%}{(\sqrt{4})\%} + 4$ Steve Wilson, 10/09Raytown, MO 1204 (3.6) $4! \times \dfrac{\sqrt{4}}{4\%} + 4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1205 (4.0) $\dfrac{4! + 4! + \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1206 (3.8) $\dfrac{4!}{(\sqrt{4})\%} + 4 + \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 1207 (4.8) $\cosh(\sqrt{4} \times \arcsch (4\%)) - 44$ Steve Wilson, 10/23Lawrence, KS 1208 (3.6) $\left( \dfrac{4!}{4\%} + 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1209 (4.0) $\dfrac{4!}{(\sqrt{4})\%} + \dfrac{4}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1210 (3.6) $\left( \sqrt{ \left( \dfrac{44}{4\%} \right)^4} \right) \pmf$ Paolo Pellegrini, 8/09Martina Franca, Italy 1211 (3.6) $\dfrac{.\overline{4} + (4 - .\overline{4}\%)\%}{4\%\%}$ Steve Wilson, 8/09Raytown, MO 1212 (4.0) $(4! + 4!\%) \times \dfrac{\sqrt{4}}{4\%}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1213 (4.2) $\dfrac{4! + (4! + \sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1214 (4.0) $\dfrac{4! + (4! + 4)\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1215 (4.0) $\dfrac{\dfrac{\sqrt{4}}{4} + 4\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1216 (3.6) $\dfrac{4!}{(\sqrt{4})\%} + 4 \times 4$ Steve Wilson, 8/09Raytown, MO 1217 (4.6) $4! \times \left( \sqrt{ .\overline{4}\%^{-4}}\right) \pm + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1218 (4.0) $\dfrac{4! + .4 - 4\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1219 (4.4) $4! \times \left( \sqrt{ .\overline{4}\%^{-4}}\right) \pm + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1220 (3.8) $(4! + .4) \times \dfrac{\sqrt{4}}{4\%}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1221 (4.2) $\dfrac{4! + .4 + (\sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1222 (3.8) $\dfrac{4! + 44\%}{(\sqrt{4})\%}$ Steve Wilson, 8/09Raytown, MO 1223 (4.2) $\dfrac{4! - (\sqrt{4})\%}{(\sqrt{4})\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1224 (3.8) $4! \times \dfrac{\sqrt{4}}{4\%} + 4!$ Paolo Pellegrini, 8/09Martina Franca, Italy 1225 (3.0) $\dfrac{4 + \dfrac{.4}{.\overline{4}}}{.4\%}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1226 (3.6) $\sqrt{ \dfrac{4}{4\%^4}} - 4!$ Steve Wilson, 8/09Raytown, MO 1227 (4.4) $\dfrac{4! + \dfrac{4!\%}{.\overline{4}}}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1228 (3.8) $\dfrac{4!}{(\sqrt{4})\%} + 4! + 4$ Steve Wilson, 8/09Raytown, MO 1229 (5.2) $\cosh(\sqrt{4} \times \arsech (4\%)) - \dfrac{4}{\sqrt{4\%}}$ Steve Wilson, 10/23Lawrence, KS 1230 (4.2) $\dfrac{ \sqrt{\sqrt{4 \pmf^{-4}}} - 4}{\sqrt{4\%}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1231 (5.0) $4! \times \left(\left( \sqrt{.\overline{4}\%^{-4}} \right) \pm + \sqrt{.\overline{4}} \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1232 (3.2) $44 \times (4! + 4)$ Paolo Pellegrini, 8/09Martina Franca, Italy 1233 (4.8) $\cosh(\sqrt{4} \times \arsech (4\%)) - 4 \times 4$ Steve Wilson, 10/23Lawrence, KS 1234 (4.2) $4 \times \left(\left(\sqrt[-.4]{4\%\%}\right)\pmm - 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1235 (4.0) $\dfrac{\sqrt{4} - 4! \pmf}{\sqrt{4\%^4}}$ Steve Wilson, 8/09Raytown, MO 1236 (4.2) $\dfrac{4! - 4!\%}{(\sqrt{4})\%} + 4!$ Steve Wilson, 10/09Raytown, MO 1237 (5.2) $\cosh(\sqrt{4} \times \arsech (4\%)) - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 10/23Lawrence, KS 1238 (4.2) $\dfrac{\sqrt{ (\sqrt{4})\%^{-4}} - 4!}{\sqrt{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1239 (4.6) $4! \times \left( \sqrt{.\overline{4}\%^{-4}} \right) \pm + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1240 (3.6) $\dfrac{4 + 4 \times 4!\%}{4 \pmf}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1241 (4.8) $\left( \sqrt[-\sqrt{.\overline{4}}]{4\%\%} \right)\% - \dfrac{4}{.\overline{4}}$ Steve Wilson, 10/09Raytown, MO 1242 (3.8) $\left( \sqrt{4\%^{-4}} - 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1243 (4.8) $\cosh(\sqrt{4} \times \arcsch (4\%)) - 4 - 4$ Steve Wilson, 10/23Lawrence, KS 1244 (3.6) $\dfrac{4!}{(\sqrt{4})\%} + 44$ Steve Wilson, 8/09Raytown, MO 1245 (3.8) $\dfrac{ \dfrac{\sqrt{4}}{4 \pmf} - \sqrt{4}}{.4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1246 (3.4) $\sqrt{ \dfrac{4}{4\%^4}} - 4$ Steve Wilson, 8/09Raytown, MO 1247 (4.8) $\cosh\left(\dfrac{4}{\sqrt{4}} \times \arcsch (4\%)\right) - 4$ Steve Wilson, 10/23Lawrence, KS 1248 (3.6) $4! \times (4! + 4! + 4)$ Paolo Pellegrini, 8/09Martina Franca, Italy 1249 (3.6) $\dfrac{ \dfrac{\sqrt{4}}{4\%\%} - 4}{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1250 (2.4) $\dfrac{4 + \dfrac44}{.4\%}$ Steve Wilson, 1/09Raytown, MO 1251 (3.6) $\dfrac{\dfrac{\sqrt{4}}{4\%\%} + 4}{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1252 (3.6) $\sqrt{ \dfrac{4}{4\%^4}} + \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 1253 (4.8) $\cosh\left(\dfrac{4}{\sqrt{4}} \times \arsech (4\%)\right) + 4$ Steve Wilson, 10/23Lawrence, KS 1254 (3.4) $\sqrt{\dfrac{4}{4\%^4}} + 4$ Steve Wilson, 8/09Raytown, MO 1255 (3.8) $\dfrac{ \dfrac{\sqrt{4}}{4 \pmf} + \sqrt{4}}{.4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1256 (3.2) $\dfrac{4}{4 \pmf} + 4^4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1257 (4.8) $\cosh(\sqrt{4} \times \arsech (4\%)) + 4 + 4$ Steve Wilson, 10/23Lawrence, KS 1258 (3.8) $\left( \sqrt{4\%^{-4}} + 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1259 (4.8) $\left(\sqrt[-\sqrt{.\overline{4}}]{4\%\%}\right)\%+\dfrac{4}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1260 (2.8) $\dfrac{4 + 4 \times .4}{.\overline{4}\%}$ Steve Wilson, 1/09Raytown, MO 1261 (5.0) $\cosh(\sqrt{4} \times \arcsch (4\%)) + \dfrac{4}{.4}$ Steve Wilson, 10/23Lawrence, KS 1262 (4.2) $\dfrac{\sqrt{(\sqrt{4})\%^{-4}} + 4!}{\sqrt{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1263 (4.6) $4! \times\left(\left(\sqrt{.\overline{4}\%^{-4}}\right)\pm+\sqrt{4}\right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1264 (4.6) $4! \times \sqrt{ \dfrac{\sqrt{.\overline{4}}}{4!\% \pmf} -4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1265 (4.0) $\dfrac{\sqrt{4} + 4! \pmf}{\sqrt{4\%^4}}$ Steve Wilson, 8/09Raytown, MO 1266 (4.2) $4 \times \left(\left( \sqrt[-.4]{4\%\%}\right)\pmm + 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1267 (4.8) $\cosh(\sqrt{4} \times \arcsch (4\%)) + 4 \times 4$ Steve Wilson, 10/23Lawrence, KS 1268 (4.0) $\dfrac{ 4^4\% - 4! \pmf}{(\sqrt{4}) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1269 (4.6) $\dfrac{4 - 4!\%}{.\overline{4}\% \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1270 (3.6) $\dfrac{4^4 - \sqrt{4}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1271 (4.8) $\dfrac{4! \times \cosh\ln 4}{4\%} - 4$ Steve Wilson, 9/23Lawrence, KS 1272 (3.4) $(4 + \sqrt{4})^4 - 4!$ Paolo Pellegrini, 8/09Martina Franca, Italy 1273 (5.0) $\dfrac{4! \times \cosh\ln 4}{4\%} - \sqrt{4}$ Steve Wilson, 10/23Lawrence, KS 1274 (3.6) $\sqrt{ \dfrac{4}{4\%^4}} + 4!$ Steve Wilson, 8/09Raytown, MO 1275 (3.8) $\dfrac{\sqrt{4} + 4\%}{\sqrt{4\%^4}}$ Steve Wilson, 8/09Raytown, MO 1276 (3.4) $\dfrac{4^4}{\sqrt{4\%}} - 4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1277 (5.0) $\dfrac{4! \times \cosh\ln 4}{4\%} + \sqrt{4}$ Steve Wilson, 10/23Lawrence, KS 1278 (3.6) $\dfrac{4^4}{\sqrt{4\%}} - \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1279 (3.8) $\dfrac{4^4 - \sqrt{4\%}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1280 (3.4) $4^4 \times \dfrac{\sqrt{4}}{.4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1281 (3.8) $\dfrac{4^4 + \sqrt{4\%}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1282 (3.6) $\dfrac{4^4}{\sqrt{4\%}} + \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1283 (5.0) $\cosh(\sqrt{4} \times \arcsch (4\%)) + \sqrt[.4]{4}$ Steve Wilson, 10/23Lawrence, KS 1284 (3.4) $\dfrac{4^4}{\sqrt{4\%}} + 4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1285 (5.0) $\dfrac{4! \times \cosh\ln 4 + .4}{4\%}$ Steve Wilson, 10/23Lawrence, KS 1286 (4.8) $\dfrac{\left(\sqrt{4!^4}\right)\pmf - .\overline{4}\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1287 (3.8) $\dfrac{ \sqrt{4!^4} - 4}{.\overline{4}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1288 (4.2) $\dfrac{\sqrt{4} + (4! \times 4!) \pmf}{(\sqrt{4}) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1289 (5.2) $\cosh(\sqrt{4} \times \arsech (4\%)) + 4\pm \times \antilog 4$ Steve Wilson, 11/23Lawrence, KS 1290 (3.6) $\dfrac{4^4 + \sqrt{4}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1291 (5.2) $\cosh(\sqrt{4} \times \arcsch (4\%)) + 4\pm \times \antilog 4$ Steve Wilson, 11/23Lawrence, KS 1292 (3.2) $(4 + \sqrt{4})^4 - 4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1293 (4.8) $\cosh(\sqrt{4} \times \arsech (4\%)) + 44$ Steve Wilson, 10/23Lawrence, KS 1294 (3.4) $(4 + \sqrt{4})^4 - \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1295 (4.2) $\dfrac{\sqrt{4!^4} - .\overline{4}}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1296 (3.2) $\left( 4 + \sqrt[\sqrt{4}]{4} \right)^4$ Paolo Pellegrini, 8/09Martina Franca, Italy 1297 (4.2) $\dfrac{\sqrt{4!^4} + .\overline{4}}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1298 (3.4) $(4 + \sqrt{4})^4 + \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1299 (4.2) $\dfrac{4! + \sqrt{4} - (\sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1300 (3.0) $\dfrac{4 + 4 \times .\overline{4}}{.\overline{4}\%}$ Paolo Pellegrini, 8/09Martina Franca, Italy 1301 (4.2) $\dfrac{4! + \sqrt{4} + (\sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1302 (4.0) $\dfrac{4! + \sqrt{4} + 4\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1303 (5.6) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 11/23Lawrence, KS 1304 (3.6) $\dfrac{4^4}{\sqrt{4\%}} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1305 (3.8) $\dfrac{\sqrt{4!^4} + 4}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1306 (4.8) $\dfrac{.\overline{4}\% + \left(\sqrt{4!^4}\right) \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1307 (5.2) $\coth\ln\coth\arcosh(4! + \sqrt{4}) - 44$ Steve Wilson, 11/23Lawrence, KS 1308 (4.8) $\dfrac{(4! + 4!\%)\% + 4!\pmf}{(\sqrt{4})\%\%}$ Steve Wilson, 11/23Lawrence, KS 1309 (5.2) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - 44$ Steve Wilson, 11/23Lawrence, KS 1310 (3.8) $\dfrac{\dfrac{\sqrt{4}}{4 \pmf} + 4!}{.4}$ Steve Wilson, 10/09Raytown, MO 1311 (4.4) $4! \times \left(\left( \sqrt{.\overline{4}\%^{-4}} \right) \pm + 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1312 (4.2) $\dfrac{4! + \sqrt{4} + 4!\%}{(\sqrt{4})\%}$ Steve Wilson, 10/09Raytown, MO 1313 (5.6) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - 4\pm \times \antilog 4$ Steve Wilson, 11/23Lawrence, KS 1314 (4.4) $\dfrac{\dfrac{4}{.\overline{4}\%} - 4!}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1315 (5.6) $\cosh(\sqrt{4} \times \arcsch (4\%)) + \sqrt{\sqrt{\sqrt{4^{4!}}}}$ Steve Wilson, 11/23Lawrence, KS 1316 (4.4) $\dfrac{4!\% + 4! \pmf}{(\sqrt{4})\%\%} - 4$ Paolo Pellegrini, 5/10Martina Franca, Italy 1317 (5.8) $\coth\ln\coth\arsech(4\%) + \sqrt{\sqrt{\sqrt{4^{4!}}}} + 4$ Steve Wilson, 11/23Lawrence, KS 1318 (4.6) $\dfrac{4!\% + 4! \pmf}{(\sqrt{4})\%\%} - \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1319 (4.8) $\dfrac{(4! - (\sqrt{4})\%)\% + 4! \pmf}{(\sqrt{4})\%\%}$ Steve Wilson, 11/23Lawrence, KS 1320 (4.0) $\sqrt{4} \times \dfrac{44}{\sqrt{.\overline{4}\%}}$ David Barksdale, 3/09Kirkland, WA 1321 (4.8) $\dfrac{(4! + (\sqrt{4})\%)\% + 4! \pmf}{(\sqrt{4})\%\%}$ Steve Wilson, 11/23Lawrence, KS 1322 (4.6) $\dfrac{4!\% + 4! \pmf}{(\sqrt{4})\%\%} + \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1323 (5.4) $\coth\ln\coth\arcosh(4! + \sqrt{4}) - 4! - 4$ Steve Wilson, 11/23Lawrence, KS 1324 (4.0) $\dfrac{4! + \sqrt{4}}{(\sqrt{4})\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1325 (4.2) $\dfrac{4! - .\overline{4}}{4 \times .\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1326 (4.0) $\dfrac{4 + \sqrt{4}}{.\overline{4}\%} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1327 (5.4) $\coth\ln\coth\arcosh\left(4! + \dfrac{4}{\sqrt{4}}\right) - 4!$ Steve Wilson, 11/23Lawrence, KS 1328 (3.8) $\dfrac{4! + 4^4\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1329 (5.4) $\coth\ln\coth\arsinh\left(4! + \dfrac{4}{\sqrt{4}}\right) - 4!$ Steve Wilson, 11/23Lawrence, KS 1330 (4.6) $\dfrac{4!\% + (4! + \sqrt{4})\pmf}{(\sqrt{4})\%\%}$ Steve Wilson, 11/23Lawrence, KS 1331 (3.8) $\sqrt{\sqrt{\sqrt{ \left( \dfrac{44}{4} \right)^{4!} }}}$ Steve Wilson, 10/09Raytown, MO 1332 (4.0) $\dfrac{4 - 4 \pmf}{\left( \sqrt{\dfrac{4}{.\overline{4}}} \right) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1333 (5.4) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - 4! + 4$ Steve Wilson, 11/23Lawrence, KS 1334 (4.2) $\dfrac{4+(\sqrt{4})\pmf}{\left(\sqrt{\dfrac{4}{.\overline{4}}}\right)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1335 (3.8) $\dfrac{ \sqrt[.4]{4} + 4\%}{4! \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1336 (4.0) $\left( \dfrac{4}{(\sqrt{4}) \pmf} + 4 \right) \times \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1337 (5.2) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - 4 \times 4$ Steve Wilson, 11/23Lawrence, KS 1338 (5.6) $\dfrac{\cot\arctan(4\%) + \sqrt{4} - 4!\%}{(\sqrt{4})\%}$ Steve Wilson, 11/23Lawrence, KS 1339 (5.6) $\coth\ln\coth\arsinh(4! + \sqrt{4}) - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 11/23Lawrence, KS 1340 (4.0) $\dfrac{ \dfrac{4!}{.\overline{4}} - .4}{4\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1341 (4.0) $\dfrac{4 + \sqrt{4} - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1342 (5.6) $\coth\ln\coth\arcosh(4! + \sqrt{4}) - \dfrac{4}{.\overline{4}}$ Steve Wilson, 11/23Lawrence, KS 1343 (5.2) $\coth\ln\coth\arcosh(4! + \sqrt{4}) - 4 - 4$ Steve Wilson, 11/23Lawrence, KS 1344 (3.6) $(4! + 4) \times (4! + 4!)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1345 (4.0) $(4 + \sqrt{4})! + \sqrt{4\%^{-4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1346 (3.8) $\dfrac{4 + \sqrt{4}}{.\overline{4}\%} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1347 (4.4) $\dfrac{ \dfrac{4}{.\overline{4}\%} - \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1348 (4.0) $\dfrac{4 + \sqrt{4}}{.\overline{4}\%} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1349 (3.8) $\dfrac{\dfrac{4!}{.\overline{4}\%} - 4}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1350 (2.8) $\dfrac{ \dfrac{4}{.4} - 4}{.\overline{4}\%}$ Steve Wilson, 1/09Raytown, MO 1351 (3.8) $\dfrac{\dfrac{4!}{.\overline{4}\%} + 4}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1352 (3.6) $\sqrt{4 \times (4! + \sqrt{4})^4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1353 (4.4) $\dfrac{\dfrac{4}{.\overline{4}\%} + \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1354 (3.8) $\dfrac{4 + \sqrt{4}}{.\overline{4}\%} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1355 (4.2) $\dfrac{ \dfrac{4!}{.\overline{4}} + \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1356 (4.2) $\dfrac{\dfrac{4}{.\overline{4}\%} + 4}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1357 (5.2) $\coth\ln\coth\arsinh\left(4! + \dfrac{4}{\sqrt{4}}\right) + 4$ Steve Wilson, 11/23Lawrence, KS 1358 (5.6) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 11/23Lawrence, KS 1359 (4.0) $\dfrac{4 + \sqrt{4} + 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1360 (4.0) $\dfrac{\dfrac{4!}{.\overline{4}} + .4}{4\%}$ Steve Wilson, 10/09Raytown, MO 1361 (5.2) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + 4 + 4$ Steve Wilson, 11/23Lawrence, KS 1362 (5.0) $\dfrac{44}{\tanh\ln\coth\arcosh 4} - \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1363 (5.4) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + \dfrac{4}{.4}$ Steve Wilson, 11/23Lawrence, KS 1364 (4.6) $44 \times \cosh( \sqrt{4} \times \arcosh 4)$ Steve Wilson, 11/23Lawrence, KS 1365 (4.6) $\dfrac{\sqrt{.\overline{4}} - (4 + \sqrt{4})\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1366 (4.8) $\dfrac{\sqrt{ \sqrt[\sqrt{.\overline{4}\%}]{4}}}{4!} + \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1367 (5.2) $\coth\ln\coth\arcosh(4! + \sqrt{4}) + 4 \times 4$ Steve Wilson, 11/23Lawrence, KS 1368 (4.4) $\dfrac{4 - \sqrt{4\%}}{\sqrt{.\overline{4}\%}} \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1369 (4.4) $\dfrac{ \sqrt{\left( 4! + \sqrt{.\overline{4}} \right)^4}}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1370 (4.4) $\dfrac{4! + \sqrt{\sqrt{4 \pm^{-4}}}}{\sqrt{4\%}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1371 (5.4) $\coth\ln\coth\arcosh(4! + \sqrt{4}) + 4! - 4$ Steve Wilson, 11/23Lawrence, KS 1372 (4.4) $\dfrac{ \sqrt[\sqrt{.\overline{4}}]{\sqrt{4} - 4\%}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1373 (5.4) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + 4! - 4$ Steve Wilson, 11/23Lawrence, KS 1374 (4.0) $\dfrac{4 + \sqrt{4}}{.\overline{4}\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1375 (3.4) $\dfrac{44}{\left( \sqrt[.4]{4} \right) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1376 (3.8) $\dfrac{4! + 4}{(\sqrt{4})\%} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1377 (5.4) $\sqrt{4 \times 4!^4} + \cot\arctan (.\overline{4}\%)$ Steve Wilson, 5/10Raytown, MO 1378 (5.6) $(4! + \sqrt{4}) \times (4 + \coth\ln\coth\arcsch\sqrt{4\%})$ Steve Wilson, 5/24Lawrence, KS 1379 (5.4) $\coth\ln\coth\arcosh(4! + \sqrt{4}) + 4! + 4$ Steve Wilson, 11/23Lawrence, KS 1380 (3.8) $\dfrac{4! + 4 - .4}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1381 (5.4) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + 4! + 4$ Steve Wilson, 11/23Lawrence, KS 1382 (4.0) $\dfrac{4!^4 \pmf}{4!\%} - .4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1383 (5.4) $\coth\ln\coth\arcosh(4! + \sqrt{4}) + \sqrt[.4]{4}$ Steve Wilson, 11/23Lawrence, KS 1384 (4.6) $\dfrac{\sqrt{.\overline{4}} + 4^4 \pmf}{\left(\sqrt{.\overline{4}} \right) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1385 (5.4) $\coth\ln\coth\arsinh(4! + \sqrt{4}) + \sqrt[.4]{4}$ Steve Wilson, 11/23Lawrence, KS 1386 (4.4) $\dfrac{ \dfrac{4}{.\overline{4}\%} + 4!}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1387 (5.6) $\coth\ln\coth\arcosh(4!) + 4!\pm \times \antilog 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1388 (4.0) $\dfrac{4! + 4 - 4!\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1389 (5.6) $\coth\ln\coth\arsinh(4!) + 4!\pm \times \antilog 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1390 (4.0) $\dfrac{4! + 4 - \sqrt{4\%}}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1391 (5.4) $\cosh(\sqrt{4} \times \arcosh(4!)) + 4!\pm \times \antilog 4$ Steve Wilson, 5/24Lawrence, KS 1392 (3.8) $4! \times \left( \dfrac{4!}{.\overline{4}} + 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1393 (5.4) $\cosh(\sqrt{4} \times \arsinh(4!)) + 4!\pm \times \antilog 4$ Steve Wilson, 5/24Lawrence, KS 1394 (5.6) $44 + \ln\sqrt{\sqrt{\exp\dfrac{4!}{.\overline{4}\%}}}$ Steve Wilson, 5/24Lawrence, KS 1395 (4.2) $\dfrac{4 + \sqrt{4} + \sqrt{4\%}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1396 (3.6) $\dfrac{4! + 4}{(\sqrt{4})\%} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1397 (5.6) $\coth\ln\coth\arsinh(4!) + 4!\pm \times \antilog 4 + 4$ Steve Wilson, 5/24Lawrence, KS 1398 (3.8) $\dfrac{4! + 4 - 4\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1399 (4.0) $\dfrac{4! + 4 - (\sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1400 (2.6) $\dfrac{4 + 4 \times .4}{.4\%}$ Steve Wilson, 1/09Raytown, MO 1401 (4.0) $\dfrac{4! + 4 + (\sqrt{4})\%}{(\sqrt{4})\%}$ Steve Wilson, 10/09Raytown, MO 1402 (3.8) $\dfrac{4! + 4 + 4\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1403 (5.4) $\dfrac{4! + 4}{(\sqrt{4})\%} + \coth\ln\sqrt{\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1404 (3.6) $\dfrac{4! + 4}{(\sqrt{4})\%} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1405 (5.4) $\dfrac{4! + 4}{(\sqrt{4})\%} + \cot\arctan\sqrt{4\%}$ Steve Wilson, 5/24Lawrence, KS 1406 (4.4) $\dfrac{\sqrt{.\overline{4}} - 4\%}{.\overline{4} \pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1407 (4.8) $\cosh(\sqrt{4} \times \arsinh (4!)) + 4^4$ Steve Wilson, 9/23Lawrence, KS 1408 (3.2) $\sqrt[.4]{4} \times 44$ Steve Wilson, 10/09Raytown, MO 1409 (4.8) $\cosh(\sqrt{4} \times \arcosh (4!)) + 4^4$ Steve Wilson, 9/23Lawrence, KS 1410 (4.0) $\dfrac{4! + 4 + \sqrt{4\%}}{(\sqrt{4})\%}$ Steve Wilson, 10/09Raytown, MO 1411 (5.0) $\coth\ln\coth\arcosh(4!) + 4^4 + 4$ Steve Wilson, 5/24Lawrence, KS 1412 (4.0) $\dfrac{4! + 4 + 4!\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1413 (5.0) $\coth\ln\coth\arsinh(4!) + 4^4 + 4$ Steve Wilson, 5/24Lawrence, KS 1414 (4.4) $\dfrac{\sqrt{.\overline{4}} - 4\%}{.\overline{4} \pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1415 (5.4) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} - \dfrac{\antilog\sqrt{4}}{4}$ Steve Wilson, 5/24Lawrence, KS 1416 (3.8) $(4 + \sqrt{4})! \times \sqrt{4} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1417 (5.8) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} - \cot\arctan(4\%) + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1418 (5.4) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} - 4! + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1419 (4.6) $\dfrac{\sqrt{.\overline{4}} - (4 - .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1420 (3.6) $\dfrac{4! + 4.4}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1421 (5.2) $\dfrac{4! + \coth\ln\coth\arsinh 4}{4\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1422 (4.6) $\dfrac{\sqrt{.4 - \sqrt{4! \pm^4}}}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1423 (5.4) $\dfrac{4! + \coth\ln\coth\arsinh 4}{4\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1424 (3.8) $\dfrac{4! + 4}{(\sqrt{4})\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1425 (4.2) $\dfrac{4! + \dfrac{\sqrt{4}}{.\overline{4}}}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1426 (4.6) $\dfrac{.\overline{4} + \sqrt{4\%}}{.\overline{4} \pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1427 (5.4) $\dfrac{4! + \coth\ln\coth\arsinh 4}{4\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1428 (4.0) $\dfrac{4! - \sqrt{4\%}}{.4} \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1429 (5.2) $\dfrac{4! + \coth\ln\coth\arsinh 4}{4\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1430 (3.6) $\dfrac{\sqrt{4!^4} - 4}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1431 (4.4) $\dfrac{.4 + (4! - .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1432 (3.6) $\left( (4 + \sqrt{4})! - 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1433 (5.8) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} - \cosh(\sqrt{4} \times \arcosh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1434 (4.6) $\dfrac{\sqrt{.\overline{4}} - 4\%}{.\overline{4} \pmf} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1435 (3.8) $\dfrac{\sqrt{4!^4} - \sqrt{4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1436 (3.6) $(4 + \sqrt{4})! \times \sqrt{4} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1437 (4.4) $\dfrac{4 \times 4! - \sqrt{4\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 10/09Raytown, MO 1438 (3.8) $(4 + \sqrt{4})! \times \sqrt{4} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1439 (3.8) $\dfrac{\sqrt{4!^4} - .4}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1440 (4.0) $4 \times 4! \times \dfrac{.4}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1441 (3.8) $\dfrac{ \sqrt{4!^4} + .4}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1442 (3.8) $(4 + \sqrt{4})! \times \sqrt{4} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1443 (4.4) $\dfrac{4 \times 4! + \sqrt{4\%}}{\sqrt{.\overline{4}\%}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1444 (3.6) $(4 + \sqrt{4})! \times \sqrt{4} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1445 (3.8) $\dfrac{\sqrt{4!^4} + \sqrt{4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1446 (4.4) $\dfrac{.\overline{4} + \sqrt{4\%}}{.\overline{4} \pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1447 (5.6) $\coth\ln\coth\arcosh(4! + 4) - \left(\dfrac{\sqrt{4}}{.4}\right)!$ Steve Wilson, 11/23Lawrence, KS 1448 (3.6) $\left( (4 + \sqrt{4})! + 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1449 (4.4) $\dfrac{.4 + (4! + .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1450 (3.8) $\dfrac{ \dfrac{4!}{.\overline{4}} + 4}{4\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1451 (5.2) $\cosh(\sqrt{4} \times \arcsch(4\%)) + \dfrac{4}{(\sqrt{4})\%}$ Steve Wilson, 11/23Lawrence, KS 1452 (4.0) $\dfrac{4! + \sqrt{4\%}}{.4} \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1453 (5.6) $\dfrac{\cosh(4 \times \arcosh\sqrt{4})}{\sqrt{.\overline{4}\%}} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1454 (4.4) $\dfrac{.\overline{4} + \sqrt{4\%}}{.\overline{4} \pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1455 (4.6) $\dfrac{\sqrt{.\overline{4}} - (4! - 4) \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1456 (3.6) $\dfrac{4!}{(\sqrt{4})\%} + 4^4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1457 (5.6) $\dfrac{\cosh(4 \times \arcosh\sqrt{4})}{\sqrt{.\overline{4}\%}} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1458 (3.8) $\sqrt{ \dfrac{ \left(\dfrac{4!}{.\overline{4}}\right)^4}{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1459 (5.4) $\dfrac{\cosh(4 \times \arcosh\sqrt{4})}{\sqrt{.\overline{4}\%}} + 4$ Steve Wilson, 5/24Lawrence, KS 1460 (4.8) $\dfrac{\sqrt{.\overline{4}} - 4 \times .\overline{4}\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1461 (5.6) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} + \cot\arctan(4\%) - 4$ Steve Wilson, 5/24Lawrence, KS 1462 (5.4) $\dfrac{4! + .4}{(\coth\ln\sqrt{4})\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1463 (5.8) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} + \cot\arctan(4\%) - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1464 (3.8) $(4 + \sqrt{4})! \times \sqrt{4} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1465 (5.4) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} + \dfrac{\antilog\sqrt{4}}{4}$ Steve Wilson, 5/24Lawrence, KS 1466 (5.0) $\dfrac{\sqrt{.\overline{4}} - .\overline{4}\%}{.\overline{4} \pmf} - 4!$ Steve Wilson, 4/24Lawrence, KS 1467 (4.6) $\dfrac{\sqrt{.\overline{4}} - 4 \pmf}{.\overline{4} \pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1468 (4.4) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} - \sqrt[.4]{4}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1469 (5.6) $\dfrac{4!}{(\coth\ln\sqrt{4})\%} + \cot\arctan(4\%) + 4$ Steve Wilson, 5/24Lawrence, KS 1470 (4.2) $\dfrac{\sqrt{4} - 4\%}{\left(\sqrt{4 \times .\overline{4}} \right) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1471 (5.2) $\coth\ln\coth\arcosh(4! + 4) - 4! \times 4$ Steve Wilson, 11/23Lawrence, KS 1472 (4.4) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} - 4! - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1473 (5.8) $\dfrac{\cosh(4 \times \arcosh\sqrt{4!}) + \sqrt{4}}{\coth\ln\sqrt{\sqrt{4}}}$ Steve Wilson, 5/24Lawrence, KS 1474 (4.2) $\sqrt[\sqrt{4\%}]{4} + \dfrac{\sqrt{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1475 (3.6) $\dfrac{4! - .4}{4 \times 4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1476 (3.6) $\dfrac{4 + \sqrt{4}}{4 \pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1477 (5.8) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{.4}{.\overline{4}\%}$ Steve Wilson, 5/24Lawrence, KS 1478 (4.6) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} - 4! + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1479 (5.4) $\dfrac{\arcsec\sqrt{4}}{(4\%)^\circ} - \cot\arctan(4\%) + 4$ Steve Wilson, 5/24Lawrence, KS 1480 (3.8) $\dfrac{.4 + 4^4\%}{(\sqrt{4}) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1481 (5.4) $4! \times \coth\ln\coth\arsinh 4 \times \sinh\ln 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1482 (4.4) $\dfrac{\sqrt{.\overline{4}} - (4 + 4) \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1483 (5.6) $4! \times \coth\ln\coth\arsinh 4 \times \sinh\ln 4 - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1484 (4.2) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} - 4 \times 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1485 (4.0) $\dfrac{4 - 4\%}{4 \pmf \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1486 (5.2) $\dfrac{(\arcsec\sqrt{4}) - (.4)^\circ}{(4\%)^\circ} - 4$ Steve Wilson, 5/24Lawrence, KS 1487 (4.4) $\dfrac{\sqrt{.\overline{4}} - 4 \pmf}{.\overline{4} \pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1488 (3.8) $4! \times \left( \dfrac{4!}{.4} + \sqrt{4} \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1489 (4.6) $\dfrac{\sqrt{.\overline{4}} - 4 \pmf}{.\overline{4} \pmf} - \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1490 (3.6) $\dfrac{4 + \sqrt{4} - 4\%}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1491 (4.4) $\dfrac{\sqrt{.\overline{44}} - 4 \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1492 (4.2) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} - 4 - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1493 (4.6) $\dfrac{\sqrt{.\overline{4}} - 4 \pmf}{.\overline{4} \pmf} + \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1494 (3.6) $\dfrac{\dfrac{4!}{4 \pmf} - 4!}{4}$ Steve Wilson, 10/09Raytown, MO 1495 (3.8) $\dfrac{4 + \sqrt{4} - (\sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1496 (3.4) $\dfrac{4 + \sqrt{4}}{4 \pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1497 (4.0) $\dfrac{ \dfrac{4}{4 \pmf} - \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1498 (3.6) $\dfrac{4 + \sqrt{4}}{4 \pmf} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1499 (3.4) $\dfrac{\dfrac{4!}{4 \pmf} - 4}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1500 (2.6) $\dfrac{\dfrac{4}{.4} - 4}{.4\%}$ Steve Wilson, 1/09Raytown, MO 1501 (3.4) $\dfrac{\dfrac{4!}{4 \pmf} + 4}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1502 (3.6) $\dfrac{4 + \sqrt{4}}{4 \pmf} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1503 (4.0) $\dfrac{\dfrac{4}{4 \pmf} + \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1504 (3.4) $\dfrac{4 + \sqrt{4}}{4 \pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1505 (3.8) $\dfrac{4 + \sqrt{4} + (\sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1506 (3.6) $\dfrac{\dfrac{4!}{4 \pmf} + 4!}{4}$ Steve Wilson, 10/09Raytown, MO 1507 (4.6) $\dfrac{\sqrt{.\overline{4}} + 4 \pmf}{.\overline{4} \pmf} - \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1508 (3.8) $\dfrac{ \left( \dfrac{4}{.4} \right)!\%}{4!} - 4$ Steve Wilson, 10/09Raytown, MO 1509 (4.4) $\dfrac{ \sqrt{.\overline{44}} + 4 \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1510 (3.6) $\dfrac{4 + \sqrt{4} + 4\%}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1511 (4.6) $\dfrac{\sqrt{.\overline{4}} + 4 \pmf}{.\overline{4} \pmf} + \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1512 (3.8) $(4! + 4) + \dfrac{4!}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1513 (4.4) $\dfrac{\sqrt{.\overline{4}} + 4 \pmf}{.\overline{4} \pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1514 (4.0) $\dfrac{\left( \dfrac{4}{.4} \right)!\%}{4!} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1515 (4.0) $\dfrac{4 + 4\%}{4 \pmf \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1516 (3.8) $\dfrac{\left( \dfrac{4}{.4} \right)!\%}{4!} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1517 (5.4) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 11/23Lawrence, KS 1518 (4.4) $\dfrac{\sqrt{.\overline{4}} + (4 + 4) \pmf}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1519 (5.4) $\coth\ln\coth\arcosh(4! + 4) - 4! \times \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1520 (3.8) $\dfrac{4 - 4! \times 4\%}{(\sqrt{4}) \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1521 (4.0) $\dfrac{\sqrt{(4! + \sqrt{4})^4}}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1522 (4.6) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} + 4! - \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1523 (5.0) $\coth\ln\coth\arcosh(4! + 4) - 44$ Steve Wilson, 11/23Lawrence, KS 1524 (3.6) $\dfrac{4 + \sqrt{4}}{4 \pmf} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1525 (3.6) $\dfrac{4! + .4}{4 \times 4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1526 (4.6) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} + 4! + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1527 (5.6) $\dfrac{\arcsec\sqrt{4}}{(4\%)^\circ} + \cot\arctan(4\%) + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1528 (4.4) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} + 4! + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1529 (5.4) $\dfrac{\arcsec\sqrt{4}}{(4\%)^\circ} + \cot\arctan(4\%) + 4$ Steve Wilson, 5/24Lawrence, KS 1530 (4.0) $\dfrac{(44 + 4!)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1531 (4.6) $\dfrac{.\overline{4} + (4! - .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1532 (4.0) $\dfrac{ \sqrt[\sqrt{4\%}]{4}}{\sqrt{.\overline{4}}} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1533 (4.2) $\dfrac{ \sqrt[\sqrt{4\%}]{4} - \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1534 (4.2) $\dfrac{ \sqrt[\sqrt{4\%}]{4}}{\sqrt{.\overline{4}}} - \sqrt{4}$ Steve Wilson, 10/09Raytown, MO 1535 (5.2) $\coth\ln\coth\arcosh(4! + 4) - \sqrt[.4]{4}$ Steve Wilson, 11/23Lawrence, KS 1536 (3.2) $4^4 \times \dfrac{4!}{4}$ Jeremy Miller, 8/07Olathe, KS 1537 (5.8) $\coth\ln\coth\arcosh(4! + 4) - \sqrt{\dfrac{4}{.\overline{4}\%}}$ Steve Wilson, 11/23Lawrence, KS 1538 (4.2) $\dfrac{ \sqrt[\sqrt{4\%}]{4}}{\sqrt{.\overline{4}}} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1539 (4.2) $\dfrac{ \sqrt[\sqrt{4\%}]{4} + \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1540 (4.0) $\dfrac{ \sqrt[\sqrt{4\%}]{4}}{\sqrt{.\overline{4}}} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1541 (5.4) $\coth\ln\coth\arcosh(4! + 4) - 4! - \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1542 (4.0) $\dfrac{ \sqrt[\sqrt{4\%}]{4} + 4}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1543 (5.0) $\cosh \left(\sqrt{4} \times \arcosh(4! + 4) \right) - 4!$ Steve Wilson, 11/23Lawrence, KS 1544 (4.2) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4} \pmf} + 44$ Paolo Pellegrini, 10/09Martina Franca, Italy 1545 (4.6) $\dfrac{\sqrt{.\overline{4}} + (4 - \sqrt{4})\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1546 (5.2) $\dfrac{(\arcsec\sqrt{4}) + (\sqrt{4})^\circ}{(4\%)^\circ} - 4$ Steve Wilson, 5/24Lawrence, KS 1547 (5.4) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{4}{\sqrt{4\%}}$ Steve Wilson, 11/23Lawrence, KS 1548 (4.2) $4! \times \left( \left( \sqrt{4 \pm^{-4}} \right) \pm + \sqrt{4} \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1549 (4.6) $\dfrac{.\overline{4} + (4! + .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1550 (3.8) $\dfrac{4 + \sqrt{4} + \sqrt{4\%}}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1551 (5.0) $\coth\ln\coth\arcosh(4! + 4) - 4 \times 4$ Steve Wilson, 11/23Lawrence, KS 1552 (5.0) $\dfrac{4}{(\cot\arctan 4)\%} - 4! - 4!$ Steve Wilson, 5/24Lawrence, KS 1553 (5.6) $\dfrac{4}{(\cot\arctan 4)\%} - \cosh(\sqrt{4} \times \arcosh\sqrt{4!})$ Steve Wilson, 5/24Lawrence, KS 1554 (5.2) $\dfrac{(\arcsec\sqrt{4}) + (\sqrt{4})^\circ}{(4\%)^\circ} + 4$ Steve Wilson, 5/24Lawrence, KS 1555 (5.4) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 11/23Lawrence, KS 1556 (4.6) $\dfrac{4}{(\cot\arctan 4)\%} - 44$ Steve Wilson, 5/24Lawrence, KS 1557 (5.2) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{4}{.4}$ Steve Wilson, 11/23Lawrence, KS 1558 (5.4) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{4}{.\overline{4}}$ Steve Wilson, 11/23Lawrence, KS 1559 (5.0) $\coth\ln\coth\arcosh(4! + 4) - 4 - 4$ Steve Wilson, 11/23Lawrence, KS 1560 (3.8) $\dfrac{4 + \sqrt{4} + 4!\%}{4 \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1561 (5.2) $\coth\ln\coth\arcosh(4! + 4) - \dfrac{4!}{4}$ Steve Wilson, 11/23Lawrence, KS 1562 (4.0) $\dfrac{(\sqrt{4})\%^{-4}\pmf - \sqrt{4}}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1563 (4.0) $\dfrac{\sqrt{4} + (\sqrt{4})\%^{-4}\pmf}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1564 (4.6) $\dfrac{.\overline{4} + 4!\%}{.\overline{4} \pmf} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1565 (4.2) $\dfrac{4 - 4!\% - 4 \pmf}{4!\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1566 (4.0) $\dfrac{(4 + \sqrt{4})! - 4!}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1567 (4.8) $\coth\ln\coth\arcosh(44 - 4 \times 4)$ Steve Wilson, 11/23Lawrence, KS 1568 (3.4) $\sqrt{4 \times (4! + 4)^4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1569 (4.8) $\cosh \left(\dfrac{4}{\sqrt{4}} \times \arsinh(4! + 4) \right)$ Steve Wilson, 11/23Lawrence, KS 1570 (5.6) $\dfrac{(4 + \sqrt{4})!}{.\overline{4}} - \cot\arctan ((\sqrt{4})\%)$ Steve Wilson, 4/10Raytown, MO 1571 (4.8) $\cosh \left(\sqrt{4} \times \arcosh(4! + 4) \right) + 4$ Steve Wilson, 11/23Lawrence, KS 1572 (4.2) $\dfrac{\sqrt[\sqrt{4\%}]{4} + 4!}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1573 (4.8) $\cosh \left(\sqrt{4} \times \arsinh(4! + 4) \right) + 4$ Steve Wilson, 11/23Lawrence, KS 1574 (5.0) $\dfrac{4}{(\cot\arctan 4)\%} - 4! - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1575 (3.8) $(4 + 4)! \times .4^{-4} \pmf$ Paolo Pellegrini, 10/09Martina Franca, Italy 1576 (3.6) $(4! - 4)^4 \% - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1577 (5.2) $\coth\ln\coth\arcosh(4! + 4) + \dfrac{4}{.4}$ Steve Wilson, 11/23Lawrence, KS 1578 (5.0) $\dfrac{4}{(\cot\arctan 4)\%} - 4! + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1579 (5.4) $\coth\ln\coth\arcosh(4! + 4) + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 11/23Lawrence, KS 1580 (4.0) $\dfrac{(4 + 4)!\% - 4!}{4!\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1581 (4.6) $\dfrac{\sqrt{.\overline{4}} + (4 - .4)\%}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1582 (5.0) $\dfrac{4 - 4\%}{(\cot\arctan 4)\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1583 (5.0) $\coth\ln\coth\arcosh(4! + 4) + 4 \times 4$ Steve Wilson, 11/23Lawrence, KS 1584 (3.8) $44 \times \dfrac{4!}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1585 (4.6) $\dfrac{(4! + \sqrt{4})\% + .\overline{4}}{.\overline{4} \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1586 (4.4) $\dfrac{\sqrt{.\overline{4}} + 4\%}{.\overline{4} \pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1587 (5.4) $\coth\ln\coth\arcosh(4! + 4) + \dfrac{4}{\sqrt{4\%}}$ Steve Wilson, 11/23Lawrence, KS 1588 (4.0) $\dfrac{\sqrt[.4]{4} - 4!\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1589 (5.4) $\coth\ln\coth\arcosh(4! + 4) + 4! - \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1590 (4.0) $\dfrac{\sqrt[.4]{4} - \sqrt{4\%}}{(\sqrt{4})\%}$ Steve Wilson, 11/09Raytown, MO 1591 (5.0) $\cosh \left(\sqrt{4} \times \arcosh(4! + 4) \right) + 4!$ Steve Wilson, 11/23Lawrence, KS 1592 (4.2) $\dfrac{4 - (\sqrt{4})\%}{\left(\sqrt{\sqrt{4^{-4}}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1593 (5.0) $\cosh \left(\sqrt{4} \times \arsinh(4! + 4) \right) + 4!$ Steve Wilson, 11/23Lawrence, KS 1594 (4.4) $\dfrac{\sqrt{.\overline{4}} + 4\%}{.\overline{4} \pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1595 (4.4) $\dfrac{4\% + (4! - \sqrt{4\%}) \pmf}{4\% \pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1596 (3.4) $(4! - 4)^4 \% - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1597 (5.8) $\coth\ln\coth\arcosh(4! + 4) + \sqrt{\dfrac{4}{.\overline{4}\%}}$ Steve Wilson, 11/23Lawrence, KS 1598 (3.6) $(4! - 4)^4 \% - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1599 (4.0) $\dfrac{\sqrt[.4]{4} - (\sqrt{4})\%}{(\sqrt{4})\%}$ Steve Wilson, 11/09Raytown, MO 1600 (2.2) $4 \times 4 \times \dfrac{4}{4\%}$ Dave Jones, 7/07Coventry, England

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