
theorem
  3037 is prime
proof
  now
    3037 = 2*1518 + 1; hence not 2 divides 3037 by NAT_4:9;
    3037 = 3*1012 + 1; hence not 3 divides 3037 by NAT_4:9;
    3037 = 5*607 + 2; hence not 5 divides 3037 by NAT_4:9;
    3037 = 7*433 + 6; hence not 7 divides 3037 by NAT_4:9;
    3037 = 11*276 + 1; hence not 11 divides 3037 by NAT_4:9;
    3037 = 13*233 + 8; hence not 13 divides 3037 by NAT_4:9;
    3037 = 17*178 + 11; hence not 17 divides 3037 by NAT_4:9;
    3037 = 19*159 + 16; hence not 19 divides 3037 by NAT_4:9;
    3037 = 23*132 + 1; hence not 23 divides 3037 by NAT_4:9;
    3037 = 29*104 + 21; hence not 29 divides 3037 by NAT_4:9;
    3037 = 31*97 + 30; hence not 31 divides 3037 by NAT_4:9;
    3037 = 37*82 + 3; hence not 37 divides 3037 by NAT_4:9;
    3037 = 41*74 + 3; hence not 41 divides 3037 by NAT_4:9;
    3037 = 43*70 + 27; hence not 43 divides 3037 by NAT_4:9;
    3037 = 47*64 + 29; hence not 47 divides 3037 by NAT_4:9;
    3037 = 53*57 + 16; hence not 53 divides 3037 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3037 & n is prime
  holds not n divides 3037 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
