
theorem
  7237 is prime
proof
  now
    7237 = 2*3618 + 1; hence not 2 divides 7237 by NAT_4:9;
    7237 = 3*2412 + 1; hence not 3 divides 7237 by NAT_4:9;
    7237 = 5*1447 + 2; hence not 5 divides 7237 by NAT_4:9;
    7237 = 7*1033 + 6; hence not 7 divides 7237 by NAT_4:9;
    7237 = 11*657 + 10; hence not 11 divides 7237 by NAT_4:9;
    7237 = 13*556 + 9; hence not 13 divides 7237 by NAT_4:9;
    7237 = 17*425 + 12; hence not 17 divides 7237 by NAT_4:9;
    7237 = 19*380 + 17; hence not 19 divides 7237 by NAT_4:9;
    7237 = 23*314 + 15; hence not 23 divides 7237 by NAT_4:9;
    7237 = 29*249 + 16; hence not 29 divides 7237 by NAT_4:9;
    7237 = 31*233 + 14; hence not 31 divides 7237 by NAT_4:9;
    7237 = 37*195 + 22; hence not 37 divides 7237 by NAT_4:9;
    7237 = 41*176 + 21; hence not 41 divides 7237 by NAT_4:9;
    7237 = 43*168 + 13; hence not 43 divides 7237 by NAT_4:9;
    7237 = 47*153 + 46; hence not 47 divides 7237 by NAT_4:9;
    7237 = 53*136 + 29; hence not 53 divides 7237 by NAT_4:9;
    7237 = 59*122 + 39; hence not 59 divides 7237 by NAT_4:9;
    7237 = 61*118 + 39; hence not 61 divides 7237 by NAT_4:9;
    7237 = 67*108 + 1; hence not 67 divides 7237 by NAT_4:9;
    7237 = 71*101 + 66; hence not 71 divides 7237 by NAT_4:9;
    7237 = 73*99 + 10; hence not 73 divides 7237 by NAT_4:9;
    7237 = 79*91 + 48; hence not 79 divides 7237 by NAT_4:9;
    7237 = 83*87 + 16; hence not 83 divides 7237 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7237 & n is prime
  holds not n divides 7237 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
