
theorem
  7649 is prime
proof
  now
    7649 = 2*3824 + 1; hence not 2 divides 7649 by NAT_4:9;
    7649 = 3*2549 + 2; hence not 3 divides 7649 by NAT_4:9;
    7649 = 5*1529 + 4; hence not 5 divides 7649 by NAT_4:9;
    7649 = 7*1092 + 5; hence not 7 divides 7649 by NAT_4:9;
    7649 = 11*695 + 4; hence not 11 divides 7649 by NAT_4:9;
    7649 = 13*588 + 5; hence not 13 divides 7649 by NAT_4:9;
    7649 = 17*449 + 16; hence not 17 divides 7649 by NAT_4:9;
    7649 = 19*402 + 11; hence not 19 divides 7649 by NAT_4:9;
    7649 = 23*332 + 13; hence not 23 divides 7649 by NAT_4:9;
    7649 = 29*263 + 22; hence not 29 divides 7649 by NAT_4:9;
    7649 = 31*246 + 23; hence not 31 divides 7649 by NAT_4:9;
    7649 = 37*206 + 27; hence not 37 divides 7649 by NAT_4:9;
    7649 = 41*186 + 23; hence not 41 divides 7649 by NAT_4:9;
    7649 = 43*177 + 38; hence not 43 divides 7649 by NAT_4:9;
    7649 = 47*162 + 35; hence not 47 divides 7649 by NAT_4:9;
    7649 = 53*144 + 17; hence not 53 divides 7649 by NAT_4:9;
    7649 = 59*129 + 38; hence not 59 divides 7649 by NAT_4:9;
    7649 = 61*125 + 24; hence not 61 divides 7649 by NAT_4:9;
    7649 = 67*114 + 11; hence not 67 divides 7649 by NAT_4:9;
    7649 = 71*107 + 52; hence not 71 divides 7649 by NAT_4:9;
    7649 = 73*104 + 57; hence not 73 divides 7649 by NAT_4:9;
    7649 = 79*96 + 65; hence not 79 divides 7649 by NAT_4:9;
    7649 = 83*92 + 13; hence not 83 divides 7649 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7649 & n is prime
  holds not n divides 7649 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
