Integermania!

First Four Naturals

The first four natural numbers are 1, 2, 3, and 4. Create each of the positive integers using one copy of each number, and any standard operations.  All four numbers must be used, but no others. Your solutions will be assigned an exquisiteness level.

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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+)

  801 (2.2)
$\dfrac{24}{3\%} + 1$
Paolo Pellegrini, 10/11
Martina Franca, Italy
802 (2.8)
$\dfrac{4 + 1\%}{(.2 + .3)\%}$
Paolo Pellegrini, 10/11
Martina Franca, Italy
803 (2.2)
$4 \times \dfrac{2}{1\%} + 3$
Paolo Pellegrini, 10/11
Martina Franca, Italy
804 (3.4)
$\dfrac{1}{2^{-3}\%} + 4$
Paolo Pellegrini, 10/11
Martina Franca, Italy
805 (3.6)
$\dfrac{4!}{3\%} + \dfrac{1}{.2}$
Paolo Pellegrini, 12/11
Martina Franca, Italy
806 (2.2)
$2 \times \left( \dfrac{4}{1\%} + 3 \right)$
Paolo Pellegrini, 10/11
Martina Franca, Italy
807 (3.6)
$\dfrac{4! + 21\%}{3\%}$
Steve Wilson, 2/12
Raytown, MO
808 (3.2)
$\dfrac{3^4}{.1} - 2$
Paolo Pellegrini, 12/11
Martina Franca, Italy
809 (4.0)
$.\overline{1}\%^{-2} ‰ - 4 + 3$
Steve Wilson, 6/12
Raytown, MO
810 (2.6)
$1.2 \times \dfrac{3}{.\overline{4}\%}$
Steve Wilson, 12/11
Raytown, MO
  811 (4.0)
$.\overline{1}\%^{-2} ‰ + 4 - 3$
Steve Wilson, 6/12
Raytown, MO
812 (2.2)
$4 \times \left( \dfrac{2}{1\%} + 3 \right)$
Paolo Pellegrini, 12/11
Martina Franca, Italy
813 (3.8)
$.\overline{1}\%^{2-4} ‰ + 3$
Steve Wilson, 6/12
Raytown, MO
814 (4.4)
$.\overline{1}\%^{-2} ‰ + 3! - \sqrt{4}$
Steve Wilson, 6/12
Raytown, MO
815 (4.2)
$.\overline{1}\%^{-2} ‰ + 3 + \sqrt{4}$
Steve Wilson, 6/12
Raytown, MO
816 (3.6)
$(1 + 2\%) \times \dfrac{4!}{3\%}$
Paolo Pellegrini, 12/11
Martina Franca, Italy
817 (4.0)
$.\overline{1}\%^{-2} ‰ + 3 + 4$
Paolo Pellegrini, 5/12
Martina Franca, Italy
818 (3.8)
$\dfrac{4!}{3\%} + \dfrac{2}{.\overline{1}}$
Steve Wilson, 2/12
Raytown, MO
819 (3.4)
$\left( 4^{3!} - 1 \right) \times .2$
Paolo Pellegrini, 2/12
Martina Franca, Italy
820 (2.2)
$\dfrac{41}{(2 + 3)\%}$
Steve Wilson, 12/11
Raytown, MO
  821 (3.4)
$\dfrac{4!}{3\%} + 21$
Steve Wilson, 2/12
Raytown, MO
822 (4.0)
$.1^{-2} + (3!)! + \sqrt{4}$
Paolo Pellegrini, 5/12
Martina Franca, Italy
823 (5.2)
$(3!)! + \dfrac{\sqrt{4}}{2\%} - \log(1 ‰)$
Steve Wilson, 10/12
Raytown, MO
824 (3.4)
$\left( \dfrac{2}{1\%} + 3! \right) \times 4$
Paolo Pellegrini, 2/12
Martina Franca, Italy
825 (2.2)
$\dfrac{31 + 2}{4\%}$
Paolo Pellegrini, 1/12
Martina Franca, Italy
826 (2.0)
$413 \times 2$
Shawn Graf, 12/06
Overland Park, KS
827 (3.2)
$\dfrac{2 \times .\overline{4} + 3\%}{.\overline{1}\%}$
Paolo Pellegrini, 1/12
Martina Franca, Italy
828 (2.4)
$23 \times \dfrac{4}{.\overline{1}}$
Paolo Pellegrini, 1/12
Martina Franca, Italy
829 (4.0)
$\sqrt{ \sqrt{ 3^{4!}}} + .1^{-2}$
Paolo Pellegrini, 5/12
Martina Franca, Italy
830 (2.4)
$\dfrac{2 \times 4 + .3}{1\%}$
Steve Wilson, 1/12
Raytown, MO
 
  831 (3.8)
$\dfrac{3}{4 ‰} + .\overline{1}^{-2}$
Paolo Pellegrini, 5/12
Martina Franca, Italy
832 (3.6)
$13 \times \sqrt{ \sqrt{ 2^{4!}}}$
Steve Wilson, 4/12
Raytown, MO
833 (3.4)
$\dfrac{4 + 1 - 2 ‰}{3! ‰}$
Paolo Pellegrini, 2/12
Martina Franca, Italy
834 (2.4)
$\dfrac{ \dfrac{1}{4\%\%} + 2}{3}$
Paolo Pellegrini, 1/12
Martina Franca, Italy
835 (2.8)
$\dfrac{1 + .2\%}{3 \times 4\%\%}$
Paolo Pellegrini, 1/12
Martina Franca, Italy
836 (3.8)
$(3!)! + \left( \dfrac{1}{.2} \right)! - 4$
Paolo Pellegrini, 6/12
Martina Franca, Italy
837 (4.4)
$\dfrac{ \dfrac{\sqrt{4\%}}{.\overline{2}\%} + 3}{.\overline{1}}$
Steve Wilson, 7/12
Raytown, MO
838 (3.6)
$(3!)! + (4 + 1)! - 2$
Steve Wilson, 5/12
Raytown, MO
839 (3.8)
$(3!)! + \left( \dfrac{2}{.4} \right)! - 1$
Paolo Pellegrini, 6/12
Martina Franca, Italy
840 (2.6)
$\dfrac{ \dfrac{1}{.4\%} + 2}{.3}$
Steve Wilson, 1/12
Raytown, MO
  841 (3.2)
$\sqrt{(31 - 2)^4}$
Paolo Pellegrini, 2/12
Martina Franca, Italy
842 (3.6)
$(3!)! + (4 + 1)! + 2$
Steve Wilson, 5/12
Raytown, MO
843 (5.2)
$(3!)! + (4 + 1)! + \coth \ln \sqrt{2}$
Steve Wilson, 10/12
Raytown, MO
844 (3.4)
$(3!)! + 124$
Paolo Pellegrini, 2/12
Martina Franca, Italy
845 (3.4)
$\dfrac{13^2}{\sqrt{4\%}}$
Paolo Pellegrini, 6/12
Martina Franca, Italy
846 (3.8)
$(3!)^4 - \dfrac{1}{.\overline{2}\%}$
Paolo Pellegrini, 6/12
Martina Franca, Italy
847 (4.8)
$(4 + 3) \times ((\cot \arctan .2)! + 1)$
Steve Wilson, 11/12
Raytown, MO
848 (3.4)
$\left( \dfrac{1}{3\%} + 2 \right) \times 4!$
Paolo Pellegrini, 6/12
Martina Franca, Italy
849 (3.6)
$\dfrac{2 - .3}{\sqrt{4} ‰} - 1$
Steve Wilson, 8/12
Raytown, MO
850 (2.2)
$\dfrac{13 + 4}{2\%}$
Steve Wilson, 1/12
Raytown, MO
  851 (3.6)
$\dfrac{2 - .3}{\sqrt{4} ‰} + 1$
Paolo Pellegrini, 7/12
Martina Franca, Italy
852 (2.0)
$213 \times 4$
Tina Redlinger, 9/07
Olathe, KS
853 (4.0)
$.\overline{1} \% ^{-2} ‰ + 43$
Paolo Pellegrini, 7/12
Martina Franca, Italy
854 (3.2)
$(.\overline{4} + 3\%) \times \dfrac{2}{.\overline{1}\%}$
Paolo Pellegrini, 3/12
Martina Franca, Italy
855 (2.8)
$\dfrac{3 + 1 - .2}{.\overline{4}\%}$
Steve Wilson, 1/12
Raytown, MO
856 (4.0)
$1 ‰ ^{-2} ‰ - 3! \times 4!$
Paolo Pellegrini, 7/12
Martina Franca, Italy
857 (4.0)
$\sqrt{ .\overline{1}\% ^{-2}} - 43$
Paolo Pellegrini, 7/12
Martina Franca, Italy
858 (3.8)
$\dfrac{3}{\sqrt{.\overline{1}} \%} - 42$
Paolo Pellegrini, 7/12
Martina Franca, Italy
859 (3.0)
$(.\overline{3}\%)^{-2} \% - 41$
Paolo Pellegrini, 10/12
Martina Franca, Italy
860 (2.2)
$43 \times \dfrac{2}{.1}$
Carolyn Neptune, 8/11
Prairie Village, KS
  861 (4.8)
$3!^2 \times 4! + \log(1 ‰)$
Steve Wilson, 11/12
Raytown, MO
862 (2.0)
$431 \times 2$
Jay Roath, 3/06
Overland Park, KS
863 (3.4)
$3!^2 \times 4! - 1$
Paolo Pellegrini, 10/12
Martina Franca, Italy
864 (2.8)
$\dfrac{3 - 2 - 4\%}{.\overline{1}\%}$
Steve Wilson, 1/12
Raytown, MO
865 (3.4)
$3!^2 \times 4! + 1$
Paolo Pellegrini, 10/12
Martina Franca, Italy
866 (3.6)
$(3!)! \times 1.2 + \sqrt{4}$
Steve Wilson, 8/12
Raytown, MO
867 (4.8)
$3!^2 \times 4! - \log(1 ‰)$
Steve Wilson, 11/12
Raytown, MO
868 (3.4)
$(3!)! \times 1.2 + 4$
Steve Wilson, 8/12
Raytown, MO
869 (3.6)
$\dfrac{21}{4! ‰} - 3!$
Steve Wilson, 9/12
Raytown, MO
870 (4.0)
$\dfrac{\sqrt{4}}{.\overline{2}\%} - \dfrac{3}{.1}$
Steve Wilson, 9/12
Raytown, MO
  871 (5.2)
$3!^2 \times 4! - \log(1 ‰ \%\%)$
Steve Wilson, 11/12
Raytown, MO
872 (3.4)
$\dfrac{21}{4! ‰} - 3$
Paolo Pellegrini, 8/12
Martina Franca, Italy
873 (3.8)
$\dfrac{ \dfrac{2}{\sqrt{4}\%} - 3}{.\overline{1}}$
Paolo Pellegrini, 8/12
Martina Franca, Italy
874 (3.6)
$\sqrt[.1]{2} - \dfrac{3}{\sqrt{4}\%}$
Paolo Pellegrini, 8/12
Martina Franca, Italy
875 (2.4)
$\dfrac{3 + \dfrac12}{.4\%}$
Steve Wilson, 3/12
Raytown, MO
876 (3.4)
$4!^2 + \dfrac{3}{1\%}$
Steve Wilson, 8/12
Raytown, MO
877 (4.2)
$(.\overline{3}\%)^{-2}\% - 4! + 1$
Steve Wilson, 11/12
Raytown, MO
878 (3.4)
$\dfrac{21}{4! ‰} + 3$
Paolo Pellegrini, 8/12
Martina Franca, Italy
879 (4.2)
$\left(\sqrt{(.\overline{3}\%)^{-4}}\right)\% - 21$
Steve Wilson, 11/12
Raytown, MO
880 (3.0)
$\dfrac{4}{(.\overline{12} + .\overline{3})\%}$
Paolo Pellegrini, 3/12
Martina Franca, Italy
  881 (3.6)
$\dfrac{21}{4! ‰} + 3!$
Paolo Pellegrini, 8/12
Martina Franca, Italy
882 (2.8)
$\dfrac{3 - 1 - 4\%}{.\overline{2}\%}$
Steve Wilson, 3/12
Raytown, MO
  884 (3.6)
$(3!)! \times 1.\overline{2} + 4$
Steve Wilson, 10/12
Raytown, MO
885 (3.6)
$(.\overline{1} + 2\%) \times \dfrac{.3}{.\overline{4}\%\%}$
Paolo Pellegrini, 10/12
Martina Franca, Italy
886 (3.0)
$(.\overline{3}\%)^{-2} \% - 14$
Paolo Pellegrini, 10/12
Martina Franca, Italy
887 (3.8)
$\dfrac{\sqrt{4}}{.\overline{2}\%} - 13$
Steve Wilson, 9/12
Raytown, MO
888 (2.8)
$\dfrac{2 + 1 - 4\%}{.\overline{3}\%}$
Steve Wilson, 3/12
Raytown, MO
889 (3.2)
$\dfrac{.\overline{4}}{(2 + 3)\%\%} + .\overline{1}$
Paolo Pellegrini, 11/12
Martina Franca, Italy
890 (3.8)
$\dfrac{ \dfrac{1}{4\%\%} - (3!)!}{2}$
Paolo Pellegrini, 11/12
Martina Franca, Italy
  891 (4.0)
$(.\overline{1}\%)^{-2} ‰ + 3^4$
Paolo Pellegrini, 11/12
Martina Franca, Italy
892 (4.0)
$(.\overline{1})^{-3} - \dfrac{4!}{.\overline{2}}$
Paolo Pellegrini, 11/12
Martina Franca, Italy
893 (4.0)
$\dfrac{\sqrt{4}}{.\overline{2}\%} - 3! - 1$
Steve Wilson, 9/12
Raytown, MO
894 (2.8)
$\dfrac{4 - 1 - 2\%}{.\overline{3}\%}$
Steve Wilson, 3/12
Raytown, MO
895 (3.6)
$\dfrac{(3!)! - 4}{1 - .2}$
Paolo Pellegrini, 11/12
Martina Franca, Italy
896 (2.6)
$\dfrac{2 + 1}{.\overline{3}\%} - 4$
Steve Wilson, 8/12
Raytown, MO
897 (3.8)
$\dfrac{\sqrt{4}}{.\overline{2}\%} - 3 \times 1$
Steve Wilson, 9/12
Raytown, MO
898 (2.6)
$\dfrac{3 + 1}{.\overline{4}\%} - 2$
Paolo Pellegrini, 3/12
Martina Franca, Italy
899 (3.4)
$(4! + 3!)^2 - 1$
Ben Kerkhoff, 7/12
Lawrence, KS
900 (2.2)
$12 \times \dfrac{3}{4\%}$
Brett Wolverton, 10/10
Overland Park, KS
  901 (3.4)
$(4! + 3!)^2 + 1$
Ben Kerkhoff, 7/12
Lawrence, KS
902 (2.6)
$\dfrac{3 + 1}{.\overline{4}\%} + 2$
Paolo Pellegrini, 3/12
Martina Franca, Italy
903 (2.0)
$21 \times 43$
Dave Jones, 10/07
Coventry, England
904 (2.6)
$\dfrac{2 + 1}{.\overline{3}\%} + 4$
Paolo Pellegrini, 3/12
Martina Franca, Italy
  906 (2.8)
$\dfrac{4 - 1 + 2\%}{.\overline{3}\%}$
Steve Wilson, 12/12
Raytown, MO
       
    912 (2.8)
$\dfrac{2 + 1 + 4\%}{.\overline{3}\%}$
Steve Wilson, 12/12
Raytown, MO
          918 (2.8)
$\dfrac{4 - 3 + 2\%}{.\overline{1}\%}$
Steve Wilson, 12/12
Raytown, MO
  920 (2.2)
$2.3 \times \dfrac{4}{1\%}$
Steve Wilson, 12/12
Raytown, MO
        924 (2.0)
$231 \times 4$
Tina Redlinger, 10/07
Olathe, KS
           
            936 (2.8)
$\dfrac{3 - 2 + 4\%}{.\overline{1}\%}$
Steve Wilson, 12/12
Raytown, MO
937 (3.2)
$31^2 - 4!$
Shannon O'Neill, 6/12
Lawrence, KS
     
      943 (2.0)
$41 \times 23$
Tina Redlinger, 10/07
Olathe, KS
  945 (2.6)
$\dfrac{3 + 1.2}{.\overline{4}\%}$
Steve Wilson, 12/12
Raytown, MO
      949 (7.2)
$(3 \times (2 + 1))!! + 4$
Jack Brewer, 9/12
Mission, KS
950 (2.4)
$\dfrac{2 + \dfrac{3}{.4} }{1\%}$
Steve Wilson, 12/12
Raytown, MO
              957 (3.0)
$31^2 - 4$
John Hepfer, 9/07
Shawnee, KS
  959 (3.2)
$\sqrt{31^4} - 2$
John Hepfer, 8/07
Shawnee, KS
960 (2.6)
$\dfrac{3 - 2 - 4\%}{.1\%}$
Steve Wilson, 12/12
Raytown, MO
      963 (3.2)
$\sqrt{31^4} + 2$
John Hepfer, 8/07
Shawnee, KS
  965 (3.0)
$31^2 + 4$
John Hepfer, 9/07
Shawnee, KS
         
    972 (3.0)
$3^4 \times 12$
Kevin Solecki, 8/08
Olathe, KS
              980 (2.6)
$\dfrac{3 - 1 - 4\%}{.2\%}$
Steve Wilson, 12/12
Raytown, MO
          985 (3.0)
$31^2 + 4!$
Wei Zhang, 6/12
Lawrence, KS
        990 (2.8)
$\dfrac{4 \times .3 + 1}{.\overline{2}\%}$
Steve Wilson, 12/12
Raytown, MO
          995 (2.6)
$\dfrac{3 + 1 - 2\%}{.4\%}$
Steve Wilson, 12/12
Raytown, MO
996 (2.4)
$\dfrac{2 + 1}{.3\%} - 4$
Steve Wilson, 12/12
Raytown, MO
  998 (2.4)
$\dfrac{3 + 1}{.4\%} - 2$
Katie Roberts, 6/12
Washington, DC
  1000 (2.2)
$\dfrac{3 \times 2 + 4}{1\%}$
Steve Wilson, 12/12
Raytown, MO
    1002 (2.4)
$\dfrac{3 + 1}{.4\%} + 2$
Steve Wilson, 7/13
Lawrence, KS
  1004 (2.4)
$\dfrac{2 + 1}{.3\%} + 4$
Steve Wilson, 7/13
Lawrence, KS
1005 (2.6)
$\dfrac{3 + 1 + 2\%}{.4\%}$
Steve Wilson, 7/13
Lawrence, KS
         
                    1020 (2.6)
$\dfrac{2.4 + 1}{.\overline{3}\%}$
Steve Wilson, 7/13
Lawrence, KS
      1023 (3.2)
$\sqrt{32^4} - 1$
John Hepfer, 8/07
Shawnee, KS
1024 (3.4)
$.1^{-3} + 24$
Eamon Devine, 7/12
Lawrence, KS
1025 (3.2)
$\sqrt{32^4} + 1$
John Hepfer, 8/07
Shawnee, KS
         
                    1040 (2.6)
$\dfrac{3 - 2 + 4\%}{.1\%}$
Steve Wilson, 7/13
Lawrence, KS
                    1050 (2.2)
$\dfrac{42}{(3 + 1)\%}$
Steve Wilson, 7/13
Lawrence, KS
    1072 (2.8)
$4 \times \left( \dfrac{.3}{.\overline{1}\%} - 2 \right)$
Steve Wilson, 7/13
Lawrence, KS
  1074 (2.8)
$3 \times \left( \dfrac{.4}{.\overline{1}\%} - 2 \right)$
Steve Wilson, 7/13
Lawrence, KS
      1078 (2.8)
$4 \times \dfrac{.3}{.\overline{1}\%} - 2$
Steve Wilson, 7/13
Lawrence, KS
  1080 (2.6)
$3 \times \dfrac{2}{(1 - .\overline{4})\%}$
Steve Wilson, 7/13
Lawrence, KS
    1082 (2.8)
$4 \times \dfrac{.3}{.\overline{1}\%} + 2$
Steve Wilson, 7/13
Lawrence, KS
      1086 (2.8)
$3 \times \left( \dfrac{.4}{.\overline{1}\%} + 2 \right)$
Steve Wilson, 7/13
Lawrence, KS
  1088 (2.8)
$4 \times \left( \dfrac{.3}{.\overline{1}\%} + 2 \right)$
Steve Wilson, 7/13
Lawrence, KS
1089 (3.0)
$(34 - 1)^2$
Tien Huynh, 9/10
Olathe, KS
 
                    1100 (2.2)
$\dfrac{4 \times 2 + 3}{1\%}$
Steve Wilson, 7/13
Lawrence, KS
                    1110 (2.8)
$\dfrac{ \dfrac{1}{.\overline{4}\%} - 3}{.2}$
Steve Wilson, 7/13
Lawrence, KS
                    1120 (2.4)
$(3 - .2) \times \dfrac{4}{1\%}$
Steve Wilson, 7/13
Lawrence, KS
    1122 (2.8)
$\dfrac{1}{.2\% \times .\overline{4}} - 3$
Steve Wilson, 7/13
Lawrence, KS
  1124 (2.6)
$\dfrac{3 + 2}{.\overline{4}\%} - 1$
Steve Wilson, 7/13
Lawrence, KS
1125 (2.6)
$\dfrac{3 + 2}{.\overline{4}\%} \times 1$
Steve Wilson, 7/13
Lawrence, KS
1126 (2.6)
$\dfrac{3 + 2}{.\overline{4}\%} + 1$
Steve Wilson, 7/13
Lawrence, KS
  1128 (2.8)
$\dfrac{1}{.2\% \times .\overline{4}} + 3$
Steve Wilson, 7/13
Lawrence, KS
   
        1134 (2.4)
$42 \times \dfrac{3}{.\overline{1}}$
Steve Wilson, 7/13
Lawrence, KS
    1137 (2.8)
$\dfrac{4 - .21}{.\overline{3}\%}$
Steve Wilson, 7/13
Lawrence, KS
  1139 (2.8)
$\dfrac{4 - .2}{.\overline{3}\%} - 1$
Steve Wilson, 7/13
Lawrence, KS
1140 (2.4)
$(4 - .2) \times \dfrac{3}{1\%}$
Steve Wilson, 7/13
Lawrence, KS
  1141 (2.8)
$\dfrac{4 - .2}{.\overline{3}\%} + 1$
Steve Wilson, 7/13
Lawrence, KS
  1143 (3.0)
$\dfrac{4 - .2 + 1\%}{.\overline{3}\%}$
Steve Wilson, 7/13
Lawrence, KS
            1150 (2.6)
$\dfrac{ \dfrac{3}{.\overline{1}} - 4}{2\%}$
Steve Wilson, 7/13
Lawrence, KS
    1152 (2.4)
$32 \times \dfrac{4}{.\overline{1}}$
Steve Wilson, 7/13
Lawrence, KS
    1155 (3.0)
$34^2 - 1$
John Hepfer, 9/07
Shawnee, KS
1156 (3.0)
$34^2 \times 1$
Melissa Kuskowski, 3/07
Olathe, KS
1157 (3.0)
$34^2 + 1$
Scott Dixon, 12/07
Lenexa, KS
     
        1164 (2.8)
$\dfrac{4 - .12}{.\overline{3}\%}$
Steve Wilson, 7/13
Lawrence, KS
      1168 (2.8)
$\dfrac{4 - .1}{.\overline{3}\%} - 2$
Steve Wilson, 7/13
Lawrence, KS
1169 (2.8)
$\dfrac{3 - .4}{.\overline{2}\%} - 1$
Steve Wilson, 7/13
Lawrence, KS
1170 (2.8)
$\dfrac{3 - .4}{.\overline{2}\%} \times 1$
Steve Wilson, 7/13
Lawrence, KS
  1171 (2.8)
$\dfrac{3 - .4}{.\overline{2}\%} + 1$
Steve Wilson, 7/13
Lawrence, KS
1172 (2.8)
$\dfrac{4 - .1}{.\overline{3}\%} + 2$
Steve Wilson, 7/13
Lawrence, KS
      1176 (3.0)
$\dfrac{4 - .1 + 2\%}{.\overline{3}\%}$
Steve Wilson, 7/13
Lawrence, KS
       
                    1200 (3.6)
$\dfrac{3! \times 4!}{12\%}$
Katie Roberts, 6/12
Washington, DC

Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-1600), Page 5 (1601+)