
theorem
  7643 is prime
proof
  now
    7643 = 2*3821 + 1; hence not 2 divides 7643 by NAT_4:9;
    7643 = 3*2547 + 2; hence not 3 divides 7643 by NAT_4:9;
    7643 = 5*1528 + 3; hence not 5 divides 7643 by NAT_4:9;
    7643 = 7*1091 + 6; hence not 7 divides 7643 by NAT_4:9;
    7643 = 11*694 + 9; hence not 11 divides 7643 by NAT_4:9;
    7643 = 13*587 + 12; hence not 13 divides 7643 by NAT_4:9;
    7643 = 17*449 + 10; hence not 17 divides 7643 by NAT_4:9;
    7643 = 19*402 + 5; hence not 19 divides 7643 by NAT_4:9;
    7643 = 23*332 + 7; hence not 23 divides 7643 by NAT_4:9;
    7643 = 29*263 + 16; hence not 29 divides 7643 by NAT_4:9;
    7643 = 31*246 + 17; hence not 31 divides 7643 by NAT_4:9;
    7643 = 37*206 + 21; hence not 37 divides 7643 by NAT_4:9;
    7643 = 41*186 + 17; hence not 41 divides 7643 by NAT_4:9;
    7643 = 43*177 + 32; hence not 43 divides 7643 by NAT_4:9;
    7643 = 47*162 + 29; hence not 47 divides 7643 by NAT_4:9;
    7643 = 53*144 + 11; hence not 53 divides 7643 by NAT_4:9;
    7643 = 59*129 + 32; hence not 59 divides 7643 by NAT_4:9;
    7643 = 61*125 + 18; hence not 61 divides 7643 by NAT_4:9;
    7643 = 67*114 + 5; hence not 67 divides 7643 by NAT_4:9;
    7643 = 71*107 + 46; hence not 71 divides 7643 by NAT_4:9;
    7643 = 73*104 + 51; hence not 73 divides 7643 by NAT_4:9;
    7643 = 79*96 + 59; hence not 79 divides 7643 by NAT_4:9;
    7643 = 83*92 + 7; hence not 83 divides 7643 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7643 & n is prime
  holds not n divides 7643 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
