
theorem
  3517 is prime
proof
  now
    3517 = 2*1758 + 1; hence not 2 divides 3517 by NAT_4:9;
    3517 = 3*1172 + 1; hence not 3 divides 3517 by NAT_4:9;
    3517 = 5*703 + 2; hence not 5 divides 3517 by NAT_4:9;
    3517 = 7*502 + 3; hence not 7 divides 3517 by NAT_4:9;
    3517 = 11*319 + 8; hence not 11 divides 3517 by NAT_4:9;
    3517 = 13*270 + 7; hence not 13 divides 3517 by NAT_4:9;
    3517 = 17*206 + 15; hence not 17 divides 3517 by NAT_4:9;
    3517 = 19*185 + 2; hence not 19 divides 3517 by NAT_4:9;
    3517 = 23*152 + 21; hence not 23 divides 3517 by NAT_4:9;
    3517 = 29*121 + 8; hence not 29 divides 3517 by NAT_4:9;
    3517 = 31*113 + 14; hence not 31 divides 3517 by NAT_4:9;
    3517 = 37*95 + 2; hence not 37 divides 3517 by NAT_4:9;
    3517 = 41*85 + 32; hence not 41 divides 3517 by NAT_4:9;
    3517 = 43*81 + 34; hence not 43 divides 3517 by NAT_4:9;
    3517 = 47*74 + 39; hence not 47 divides 3517 by NAT_4:9;
    3517 = 53*66 + 19; hence not 53 divides 3517 by NAT_4:9;
    3517 = 59*59 + 36; hence not 59 divides 3517 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3517 & n is prime
  holds not n divides 3517 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
