
theorem
  7883 is prime
proof
  now
    7883 = 2*3941 + 1; hence not 2 divides 7883 by NAT_4:9;
    7883 = 3*2627 + 2; hence not 3 divides 7883 by NAT_4:9;
    7883 = 5*1576 + 3; hence not 5 divides 7883 by NAT_4:9;
    7883 = 7*1126 + 1; hence not 7 divides 7883 by NAT_4:9;
    7883 = 11*716 + 7; hence not 11 divides 7883 by NAT_4:9;
    7883 = 13*606 + 5; hence not 13 divides 7883 by NAT_4:9;
    7883 = 17*463 + 12; hence not 17 divides 7883 by NAT_4:9;
    7883 = 19*414 + 17; hence not 19 divides 7883 by NAT_4:9;
    7883 = 23*342 + 17; hence not 23 divides 7883 by NAT_4:9;
    7883 = 29*271 + 24; hence not 29 divides 7883 by NAT_4:9;
    7883 = 31*254 + 9; hence not 31 divides 7883 by NAT_4:9;
    7883 = 37*213 + 2; hence not 37 divides 7883 by NAT_4:9;
    7883 = 41*192 + 11; hence not 41 divides 7883 by NAT_4:9;
    7883 = 43*183 + 14; hence not 43 divides 7883 by NAT_4:9;
    7883 = 47*167 + 34; hence not 47 divides 7883 by NAT_4:9;
    7883 = 53*148 + 39; hence not 53 divides 7883 by NAT_4:9;
    7883 = 59*133 + 36; hence not 59 divides 7883 by NAT_4:9;
    7883 = 61*129 + 14; hence not 61 divides 7883 by NAT_4:9;
    7883 = 67*117 + 44; hence not 67 divides 7883 by NAT_4:9;
    7883 = 71*111 + 2; hence not 71 divides 7883 by NAT_4:9;
    7883 = 73*107 + 72; hence not 73 divides 7883 by NAT_4:9;
    7883 = 79*99 + 62; hence not 79 divides 7883 by NAT_4:9;
    7883 = 83*94 + 81; hence not 83 divides 7883 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7883 & n is prime
  holds not n divides 7883 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
