
theorem
  7417 is prime
proof
  now
    7417 = 2*3708 + 1; hence not 2 divides 7417 by NAT_4:9;
    7417 = 3*2472 + 1; hence not 3 divides 7417 by NAT_4:9;
    7417 = 5*1483 + 2; hence not 5 divides 7417 by NAT_4:9;
    7417 = 7*1059 + 4; hence not 7 divides 7417 by NAT_4:9;
    7417 = 11*674 + 3; hence not 11 divides 7417 by NAT_4:9;
    7417 = 13*570 + 7; hence not 13 divides 7417 by NAT_4:9;
    7417 = 17*436 + 5; hence not 17 divides 7417 by NAT_4:9;
    7417 = 19*390 + 7; hence not 19 divides 7417 by NAT_4:9;
    7417 = 23*322 + 11; hence not 23 divides 7417 by NAT_4:9;
    7417 = 29*255 + 22; hence not 29 divides 7417 by NAT_4:9;
    7417 = 31*239 + 8; hence not 31 divides 7417 by NAT_4:9;
    7417 = 37*200 + 17; hence not 37 divides 7417 by NAT_4:9;
    7417 = 41*180 + 37; hence not 41 divides 7417 by NAT_4:9;
    7417 = 43*172 + 21; hence not 43 divides 7417 by NAT_4:9;
    7417 = 47*157 + 38; hence not 47 divides 7417 by NAT_4:9;
    7417 = 53*139 + 50; hence not 53 divides 7417 by NAT_4:9;
    7417 = 59*125 + 42; hence not 59 divides 7417 by NAT_4:9;
    7417 = 61*121 + 36; hence not 61 divides 7417 by NAT_4:9;
    7417 = 67*110 + 47; hence not 67 divides 7417 by NAT_4:9;
    7417 = 71*104 + 33; hence not 71 divides 7417 by NAT_4:9;
    7417 = 73*101 + 44; hence not 73 divides 7417 by NAT_4:9;
    7417 = 79*93 + 70; hence not 79 divides 7417 by NAT_4:9;
    7417 = 83*89 + 30; hence not 83 divides 7417 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7417 & n is prime
  holds not n divides 7417 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
