
theorem
  3137 is prime
proof
  now
    3137 = 2*1568 + 1; hence not 2 divides 3137 by NAT_4:9;
    3137 = 3*1045 + 2; hence not 3 divides 3137 by NAT_4:9;
    3137 = 5*627 + 2; hence not 5 divides 3137 by NAT_4:9;
    3137 = 7*448 + 1; hence not 7 divides 3137 by NAT_4:9;
    3137 = 11*285 + 2; hence not 11 divides 3137 by NAT_4:9;
    3137 = 13*241 + 4; hence not 13 divides 3137 by NAT_4:9;
    3137 = 17*184 + 9; hence not 17 divides 3137 by NAT_4:9;
    3137 = 19*165 + 2; hence not 19 divides 3137 by NAT_4:9;
    3137 = 23*136 + 9; hence not 23 divides 3137 by NAT_4:9;
    3137 = 29*108 + 5; hence not 29 divides 3137 by NAT_4:9;
    3137 = 31*101 + 6; hence not 31 divides 3137 by NAT_4:9;
    3137 = 37*84 + 29; hence not 37 divides 3137 by NAT_4:9;
    3137 = 41*76 + 21; hence not 41 divides 3137 by NAT_4:9;
    3137 = 43*72 + 41; hence not 43 divides 3137 by NAT_4:9;
    3137 = 47*66 + 35; hence not 47 divides 3137 by NAT_4:9;
    3137 = 53*59 + 10; hence not 53 divides 3137 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3137 & n is prime
  holds not n divides 3137 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
