
theorem
  3491 is prime
proof
  now
    3491 = 2*1745 + 1; hence not 2 divides 3491 by NAT_4:9;
    3491 = 3*1163 + 2; hence not 3 divides 3491 by NAT_4:9;
    3491 = 5*698 + 1; hence not 5 divides 3491 by NAT_4:9;
    3491 = 7*498 + 5; hence not 7 divides 3491 by NAT_4:9;
    3491 = 11*317 + 4; hence not 11 divides 3491 by NAT_4:9;
    3491 = 13*268 + 7; hence not 13 divides 3491 by NAT_4:9;
    3491 = 17*205 + 6; hence not 17 divides 3491 by NAT_4:9;
    3491 = 19*183 + 14; hence not 19 divides 3491 by NAT_4:9;
    3491 = 23*151 + 18; hence not 23 divides 3491 by NAT_4:9;
    3491 = 29*120 + 11; hence not 29 divides 3491 by NAT_4:9;
    3491 = 31*112 + 19; hence not 31 divides 3491 by NAT_4:9;
    3491 = 37*94 + 13; hence not 37 divides 3491 by NAT_4:9;
    3491 = 41*85 + 6; hence not 41 divides 3491 by NAT_4:9;
    3491 = 43*81 + 8; hence not 43 divides 3491 by NAT_4:9;
    3491 = 47*74 + 13; hence not 47 divides 3491 by NAT_4:9;
    3491 = 53*65 + 46; hence not 53 divides 3491 by NAT_4:9;
    3491 = 59*59 + 10; hence not 59 divides 3491 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3491 & n is prime
  holds not n divides 3491 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
