
theorem
  7121 is prime
proof
  now
    7121 = 2*3560 + 1; hence not 2 divides 7121 by NAT_4:9;
    7121 = 3*2373 + 2; hence not 3 divides 7121 by NAT_4:9;
    7121 = 5*1424 + 1; hence not 5 divides 7121 by NAT_4:9;
    7121 = 7*1017 + 2; hence not 7 divides 7121 by NAT_4:9;
    7121 = 11*647 + 4; hence not 11 divides 7121 by NAT_4:9;
    7121 = 13*547 + 10; hence not 13 divides 7121 by NAT_4:9;
    7121 = 17*418 + 15; hence not 17 divides 7121 by NAT_4:9;
    7121 = 19*374 + 15; hence not 19 divides 7121 by NAT_4:9;
    7121 = 23*309 + 14; hence not 23 divides 7121 by NAT_4:9;
    7121 = 29*245 + 16; hence not 29 divides 7121 by NAT_4:9;
    7121 = 31*229 + 22; hence not 31 divides 7121 by NAT_4:9;
    7121 = 37*192 + 17; hence not 37 divides 7121 by NAT_4:9;
    7121 = 41*173 + 28; hence not 41 divides 7121 by NAT_4:9;
    7121 = 43*165 + 26; hence not 43 divides 7121 by NAT_4:9;
    7121 = 47*151 + 24; hence not 47 divides 7121 by NAT_4:9;
    7121 = 53*134 + 19; hence not 53 divides 7121 by NAT_4:9;
    7121 = 59*120 + 41; hence not 59 divides 7121 by NAT_4:9;
    7121 = 61*116 + 45; hence not 61 divides 7121 by NAT_4:9;
    7121 = 67*106 + 19; hence not 67 divides 7121 by NAT_4:9;
    7121 = 71*100 + 21; hence not 71 divides 7121 by NAT_4:9;
    7121 = 73*97 + 40; hence not 73 divides 7121 by NAT_4:9;
    7121 = 79*90 + 11; hence not 79 divides 7121 by NAT_4:9;
    7121 = 83*85 + 66; hence not 83 divides 7121 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7121 & n is prime
  holds not n divides 7121 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
