
theorem
  4759 is prime
proof
  now
    4759 = 2*2379 + 1; hence not 2 divides 4759 by NAT_4:9;
    4759 = 3*1586 + 1; hence not 3 divides 4759 by NAT_4:9;
    4759 = 5*951 + 4; hence not 5 divides 4759 by NAT_4:9;
    4759 = 7*679 + 6; hence not 7 divides 4759 by NAT_4:9;
    4759 = 11*432 + 7; hence not 11 divides 4759 by NAT_4:9;
    4759 = 13*366 + 1; hence not 13 divides 4759 by NAT_4:9;
    4759 = 17*279 + 16; hence not 17 divides 4759 by NAT_4:9;
    4759 = 19*250 + 9; hence not 19 divides 4759 by NAT_4:9;
    4759 = 23*206 + 21; hence not 23 divides 4759 by NAT_4:9;
    4759 = 29*164 + 3; hence not 29 divides 4759 by NAT_4:9;
    4759 = 31*153 + 16; hence not 31 divides 4759 by NAT_4:9;
    4759 = 37*128 + 23; hence not 37 divides 4759 by NAT_4:9;
    4759 = 41*116 + 3; hence not 41 divides 4759 by NAT_4:9;
    4759 = 43*110 + 29; hence not 43 divides 4759 by NAT_4:9;
    4759 = 47*101 + 12; hence not 47 divides 4759 by NAT_4:9;
    4759 = 53*89 + 42; hence not 53 divides 4759 by NAT_4:9;
    4759 = 59*80 + 39; hence not 59 divides 4759 by NAT_4:9;
    4759 = 61*78 + 1; hence not 61 divides 4759 by NAT_4:9;
    4759 = 67*71 + 2; hence not 67 divides 4759 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4759 & n is prime
  holds not n divides 4759 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
