
theorem
  4951 is prime
proof
  now
    4951 = 2*2475 + 1; hence not 2 divides 4951 by NAT_4:9;
    4951 = 3*1650 + 1; hence not 3 divides 4951 by NAT_4:9;
    4951 = 5*990 + 1; hence not 5 divides 4951 by NAT_4:9;
    4951 = 7*707 + 2; hence not 7 divides 4951 by NAT_4:9;
    4951 = 11*450 + 1; hence not 11 divides 4951 by NAT_4:9;
    4951 = 13*380 + 11; hence not 13 divides 4951 by NAT_4:9;
    4951 = 17*291 + 4; hence not 17 divides 4951 by NAT_4:9;
    4951 = 19*260 + 11; hence not 19 divides 4951 by NAT_4:9;
    4951 = 23*215 + 6; hence not 23 divides 4951 by NAT_4:9;
    4951 = 29*170 + 21; hence not 29 divides 4951 by NAT_4:9;
    4951 = 31*159 + 22; hence not 31 divides 4951 by NAT_4:9;
    4951 = 37*133 + 30; hence not 37 divides 4951 by NAT_4:9;
    4951 = 41*120 + 31; hence not 41 divides 4951 by NAT_4:9;
    4951 = 43*115 + 6; hence not 43 divides 4951 by NAT_4:9;
    4951 = 47*105 + 16; hence not 47 divides 4951 by NAT_4:9;
    4951 = 53*93 + 22; hence not 53 divides 4951 by NAT_4:9;
    4951 = 59*83 + 54; hence not 59 divides 4951 by NAT_4:9;
    4951 = 61*81 + 10; hence not 61 divides 4951 by NAT_4:9;
    4951 = 67*73 + 60; hence not 67 divides 4951 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4951 & n is prime
  holds not n divides 4951 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
