
theorem
  3511 is prime
proof
  now
    3511 = 2*1755 + 1; hence not 2 divides 3511 by NAT_4:9;
    3511 = 3*1170 + 1; hence not 3 divides 3511 by NAT_4:9;
    3511 = 5*702 + 1; hence not 5 divides 3511 by NAT_4:9;
    3511 = 7*501 + 4; hence not 7 divides 3511 by NAT_4:9;
    3511 = 11*319 + 2; hence not 11 divides 3511 by NAT_4:9;
    3511 = 13*270 + 1; hence not 13 divides 3511 by NAT_4:9;
    3511 = 17*206 + 9; hence not 17 divides 3511 by NAT_4:9;
    3511 = 19*184 + 15; hence not 19 divides 3511 by NAT_4:9;
    3511 = 23*152 + 15; hence not 23 divides 3511 by NAT_4:9;
    3511 = 29*121 + 2; hence not 29 divides 3511 by NAT_4:9;
    3511 = 31*113 + 8; hence not 31 divides 3511 by NAT_4:9;
    3511 = 37*94 + 33; hence not 37 divides 3511 by NAT_4:9;
    3511 = 41*85 + 26; hence not 41 divides 3511 by NAT_4:9;
    3511 = 43*81 + 28; hence not 43 divides 3511 by NAT_4:9;
    3511 = 47*74 + 33; hence not 47 divides 3511 by NAT_4:9;
    3511 = 53*66 + 13; hence not 53 divides 3511 by NAT_4:9;
    3511 = 59*59 + 30; hence not 59 divides 3511 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3511 & n is prime
  holds not n divides 3511 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
