
theorem
  7351 is prime
proof
  now
    7351 = 2*3675 + 1; hence not 2 divides 7351 by NAT_4:9;
    7351 = 3*2450 + 1; hence not 3 divides 7351 by NAT_4:9;
    7351 = 5*1470 + 1; hence not 5 divides 7351 by NAT_4:9;
    7351 = 7*1050 + 1; hence not 7 divides 7351 by NAT_4:9;
    7351 = 11*668 + 3; hence not 11 divides 7351 by NAT_4:9;
    7351 = 13*565 + 6; hence not 13 divides 7351 by NAT_4:9;
    7351 = 17*432 + 7; hence not 17 divides 7351 by NAT_4:9;
    7351 = 19*386 + 17; hence not 19 divides 7351 by NAT_4:9;
    7351 = 23*319 + 14; hence not 23 divides 7351 by NAT_4:9;
    7351 = 29*253 + 14; hence not 29 divides 7351 by NAT_4:9;
    7351 = 31*237 + 4; hence not 31 divides 7351 by NAT_4:9;
    7351 = 37*198 + 25; hence not 37 divides 7351 by NAT_4:9;
    7351 = 41*179 + 12; hence not 41 divides 7351 by NAT_4:9;
    7351 = 43*170 + 41; hence not 43 divides 7351 by NAT_4:9;
    7351 = 47*156 + 19; hence not 47 divides 7351 by NAT_4:9;
    7351 = 53*138 + 37; hence not 53 divides 7351 by NAT_4:9;
    7351 = 59*124 + 35; hence not 59 divides 7351 by NAT_4:9;
    7351 = 61*120 + 31; hence not 61 divides 7351 by NAT_4:9;
    7351 = 67*109 + 48; hence not 67 divides 7351 by NAT_4:9;
    7351 = 71*103 + 38; hence not 71 divides 7351 by NAT_4:9;
    7351 = 73*100 + 51; hence not 73 divides 7351 by NAT_4:9;
    7351 = 79*93 + 4; hence not 79 divides 7351 by NAT_4:9;
    7351 = 83*88 + 47; hence not 83 divides 7351 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7351 & n is prime
  holds not n divides 7351 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
