
theorem
  3187 is prime
proof
  now
    3187 = 2*1593 + 1; hence not 2 divides 3187 by NAT_4:9;
    3187 = 3*1062 + 1; hence not 3 divides 3187 by NAT_4:9;
    3187 = 5*637 + 2; hence not 5 divides 3187 by NAT_4:9;
    3187 = 7*455 + 2; hence not 7 divides 3187 by NAT_4:9;
    3187 = 11*289 + 8; hence not 11 divides 3187 by NAT_4:9;
    3187 = 13*245 + 2; hence not 13 divides 3187 by NAT_4:9;
    3187 = 17*187 + 8; hence not 17 divides 3187 by NAT_4:9;
    3187 = 19*167 + 14; hence not 19 divides 3187 by NAT_4:9;
    3187 = 23*138 + 13; hence not 23 divides 3187 by NAT_4:9;
    3187 = 29*109 + 26; hence not 29 divides 3187 by NAT_4:9;
    3187 = 31*102 + 25; hence not 31 divides 3187 by NAT_4:9;
    3187 = 37*86 + 5; hence not 37 divides 3187 by NAT_4:9;
    3187 = 41*77 + 30; hence not 41 divides 3187 by NAT_4:9;
    3187 = 43*74 + 5; hence not 43 divides 3187 by NAT_4:9;
    3187 = 47*67 + 38; hence not 47 divides 3187 by NAT_4:9;
    3187 = 53*60 + 7; hence not 53 divides 3187 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3187 & n is prime
  holds not n divides 3187 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
