
theorem
  5279 is prime
proof
  now
    5279 = 2*2639 + 1; hence not 2 divides 5279 by NAT_4:9;
    5279 = 3*1759 + 2; hence not 3 divides 5279 by NAT_4:9;
    5279 = 5*1055 + 4; hence not 5 divides 5279 by NAT_4:9;
    5279 = 7*754 + 1; hence not 7 divides 5279 by NAT_4:9;
    5279 = 11*479 + 10; hence not 11 divides 5279 by NAT_4:9;
    5279 = 13*406 + 1; hence not 13 divides 5279 by NAT_4:9;
    5279 = 17*310 + 9; hence not 17 divides 5279 by NAT_4:9;
    5279 = 19*277 + 16; hence not 19 divides 5279 by NAT_4:9;
    5279 = 23*229 + 12; hence not 23 divides 5279 by NAT_4:9;
    5279 = 29*182 + 1; hence not 29 divides 5279 by NAT_4:9;
    5279 = 31*170 + 9; hence not 31 divides 5279 by NAT_4:9;
    5279 = 37*142 + 25; hence not 37 divides 5279 by NAT_4:9;
    5279 = 41*128 + 31; hence not 41 divides 5279 by NAT_4:9;
    5279 = 43*122 + 33; hence not 43 divides 5279 by NAT_4:9;
    5279 = 47*112 + 15; hence not 47 divides 5279 by NAT_4:9;
    5279 = 53*99 + 32; hence not 53 divides 5279 by NAT_4:9;
    5279 = 59*89 + 28; hence not 59 divides 5279 by NAT_4:9;
    5279 = 61*86 + 33; hence not 61 divides 5279 by NAT_4:9;
    5279 = 67*78 + 53; hence not 67 divides 5279 by NAT_4:9;
    5279 = 71*74 + 25; hence not 71 divides 5279 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5279 & n is prime
  holds not n divides 5279 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
