
theorem
  4751 is prime
proof
  now
    4751 = 2*2375 + 1; hence not 2 divides 4751 by NAT_4:9;
    4751 = 3*1583 + 2; hence not 3 divides 4751 by NAT_4:9;
    4751 = 5*950 + 1; hence not 5 divides 4751 by NAT_4:9;
    4751 = 7*678 + 5; hence not 7 divides 4751 by NAT_4:9;
    4751 = 11*431 + 10; hence not 11 divides 4751 by NAT_4:9;
    4751 = 13*365 + 6; hence not 13 divides 4751 by NAT_4:9;
    4751 = 17*279 + 8; hence not 17 divides 4751 by NAT_4:9;
    4751 = 19*250 + 1; hence not 19 divides 4751 by NAT_4:9;
    4751 = 23*206 + 13; hence not 23 divides 4751 by NAT_4:9;
    4751 = 29*163 + 24; hence not 29 divides 4751 by NAT_4:9;
    4751 = 31*153 + 8; hence not 31 divides 4751 by NAT_4:9;
    4751 = 37*128 + 15; hence not 37 divides 4751 by NAT_4:9;
    4751 = 41*115 + 36; hence not 41 divides 4751 by NAT_4:9;
    4751 = 43*110 + 21; hence not 43 divides 4751 by NAT_4:9;
    4751 = 47*101 + 4; hence not 47 divides 4751 by NAT_4:9;
    4751 = 53*89 + 34; hence not 53 divides 4751 by NAT_4:9;
    4751 = 59*80 + 31; hence not 59 divides 4751 by NAT_4:9;
    4751 = 61*77 + 54; hence not 61 divides 4751 by NAT_4:9;
    4751 = 67*70 + 61; hence not 67 divides 4751 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4751 & n is prime
  holds not n divides 4751 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
