
theorem
  6637 is prime
proof
  now
    6637 = 2*3318 + 1; hence not 2 divides 6637 by NAT_4:9;
    6637 = 3*2212 + 1; hence not 3 divides 6637 by NAT_4:9;
    6637 = 5*1327 + 2; hence not 5 divides 6637 by NAT_4:9;
    6637 = 7*948 + 1; hence not 7 divides 6637 by NAT_4:9;
    6637 = 11*603 + 4; hence not 11 divides 6637 by NAT_4:9;
    6637 = 13*510 + 7; hence not 13 divides 6637 by NAT_4:9;
    6637 = 17*390 + 7; hence not 17 divides 6637 by NAT_4:9;
    6637 = 19*349 + 6; hence not 19 divides 6637 by NAT_4:9;
    6637 = 23*288 + 13; hence not 23 divides 6637 by NAT_4:9;
    6637 = 29*228 + 25; hence not 29 divides 6637 by NAT_4:9;
    6637 = 31*214 + 3; hence not 31 divides 6637 by NAT_4:9;
    6637 = 37*179 + 14; hence not 37 divides 6637 by NAT_4:9;
    6637 = 41*161 + 36; hence not 41 divides 6637 by NAT_4:9;
    6637 = 43*154 + 15; hence not 43 divides 6637 by NAT_4:9;
    6637 = 47*141 + 10; hence not 47 divides 6637 by NAT_4:9;
    6637 = 53*125 + 12; hence not 53 divides 6637 by NAT_4:9;
    6637 = 59*112 + 29; hence not 59 divides 6637 by NAT_4:9;
    6637 = 61*108 + 49; hence not 61 divides 6637 by NAT_4:9;
    6637 = 67*99 + 4; hence not 67 divides 6637 by NAT_4:9;
    6637 = 71*93 + 34; hence not 71 divides 6637 by NAT_4:9;
    6637 = 73*90 + 67; hence not 73 divides 6637 by NAT_4:9;
    6637 = 79*84 + 1; hence not 79 divides 6637 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6637 & n is prime
  holds not n divides 6637 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
