
theorem
  7459 is prime
proof
  now
    7459 = 2*3729 + 1; hence not 2 divides 7459 by NAT_4:9;
    7459 = 3*2486 + 1; hence not 3 divides 7459 by NAT_4:9;
    7459 = 5*1491 + 4; hence not 5 divides 7459 by NAT_4:9;
    7459 = 7*1065 + 4; hence not 7 divides 7459 by NAT_4:9;
    7459 = 11*678 + 1; hence not 11 divides 7459 by NAT_4:9;
    7459 = 13*573 + 10; hence not 13 divides 7459 by NAT_4:9;
    7459 = 17*438 + 13; hence not 17 divides 7459 by NAT_4:9;
    7459 = 19*392 + 11; hence not 19 divides 7459 by NAT_4:9;
    7459 = 23*324 + 7; hence not 23 divides 7459 by NAT_4:9;
    7459 = 29*257 + 6; hence not 29 divides 7459 by NAT_4:9;
    7459 = 31*240 + 19; hence not 31 divides 7459 by NAT_4:9;
    7459 = 37*201 + 22; hence not 37 divides 7459 by NAT_4:9;
    7459 = 41*181 + 38; hence not 41 divides 7459 by NAT_4:9;
    7459 = 43*173 + 20; hence not 43 divides 7459 by NAT_4:9;
    7459 = 47*158 + 33; hence not 47 divides 7459 by NAT_4:9;
    7459 = 53*140 + 39; hence not 53 divides 7459 by NAT_4:9;
    7459 = 59*126 + 25; hence not 59 divides 7459 by NAT_4:9;
    7459 = 61*122 + 17; hence not 61 divides 7459 by NAT_4:9;
    7459 = 67*111 + 22; hence not 67 divides 7459 by NAT_4:9;
    7459 = 71*105 + 4; hence not 71 divides 7459 by NAT_4:9;
    7459 = 73*102 + 13; hence not 73 divides 7459 by NAT_4:9;
    7459 = 79*94 + 33; hence not 79 divides 7459 by NAT_4:9;
    7459 = 83*89 + 72; hence not 83 divides 7459 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7459 & n is prime
  holds not n divides 7459 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
