
theorem
  5783 is prime
proof
  now
    5783 = 2*2891 + 1; hence not 2 divides 5783 by NAT_4:9;
    5783 = 3*1927 + 2; hence not 3 divides 5783 by NAT_4:9;
    5783 = 5*1156 + 3; hence not 5 divides 5783 by NAT_4:9;
    5783 = 7*826 + 1; hence not 7 divides 5783 by NAT_4:9;
    5783 = 11*525 + 8; hence not 11 divides 5783 by NAT_4:9;
    5783 = 13*444 + 11; hence not 13 divides 5783 by NAT_4:9;
    5783 = 17*340 + 3; hence not 17 divides 5783 by NAT_4:9;
    5783 = 19*304 + 7; hence not 19 divides 5783 by NAT_4:9;
    5783 = 23*251 + 10; hence not 23 divides 5783 by NAT_4:9;
    5783 = 29*199 + 12; hence not 29 divides 5783 by NAT_4:9;
    5783 = 31*186 + 17; hence not 31 divides 5783 by NAT_4:9;
    5783 = 37*156 + 11; hence not 37 divides 5783 by NAT_4:9;
    5783 = 41*141 + 2; hence not 41 divides 5783 by NAT_4:9;
    5783 = 43*134 + 21; hence not 43 divides 5783 by NAT_4:9;
    5783 = 47*123 + 2; hence not 47 divides 5783 by NAT_4:9;
    5783 = 53*109 + 6; hence not 53 divides 5783 by NAT_4:9;
    5783 = 59*98 + 1; hence not 59 divides 5783 by NAT_4:9;
    5783 = 61*94 + 49; hence not 61 divides 5783 by NAT_4:9;
    5783 = 67*86 + 21; hence not 67 divides 5783 by NAT_4:9;
    5783 = 71*81 + 32; hence not 71 divides 5783 by NAT_4:9;
    5783 = 73*79 + 16; hence not 73 divides 5783 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5783 & n is prime
  holds not n divides 5783 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
