
theorem
  6151 is prime
proof
  now
    6151 = 2*3075 + 1; hence not 2 divides 6151 by NAT_4:9;
    6151 = 3*2050 + 1; hence not 3 divides 6151 by NAT_4:9;
    6151 = 5*1230 + 1; hence not 5 divides 6151 by NAT_4:9;
    6151 = 7*878 + 5; hence not 7 divides 6151 by NAT_4:9;
    6151 = 11*559 + 2; hence not 11 divides 6151 by NAT_4:9;
    6151 = 13*473 + 2; hence not 13 divides 6151 by NAT_4:9;
    6151 = 17*361 + 14; hence not 17 divides 6151 by NAT_4:9;
    6151 = 19*323 + 14; hence not 19 divides 6151 by NAT_4:9;
    6151 = 23*267 + 10; hence not 23 divides 6151 by NAT_4:9;
    6151 = 29*212 + 3; hence not 29 divides 6151 by NAT_4:9;
    6151 = 31*198 + 13; hence not 31 divides 6151 by NAT_4:9;
    6151 = 37*166 + 9; hence not 37 divides 6151 by NAT_4:9;
    6151 = 41*150 + 1; hence not 41 divides 6151 by NAT_4:9;
    6151 = 43*143 + 2; hence not 43 divides 6151 by NAT_4:9;
    6151 = 47*130 + 41; hence not 47 divides 6151 by NAT_4:9;
    6151 = 53*116 + 3; hence not 53 divides 6151 by NAT_4:9;
    6151 = 59*104 + 15; hence not 59 divides 6151 by NAT_4:9;
    6151 = 61*100 + 51; hence not 61 divides 6151 by NAT_4:9;
    6151 = 67*91 + 54; hence not 67 divides 6151 by NAT_4:9;
    6151 = 71*86 + 45; hence not 71 divides 6151 by NAT_4:9;
    6151 = 73*84 + 19; hence not 73 divides 6151 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6151 & n is prime
  holds not n divides 6151 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
