
theorem
  4969 is prime
proof
  now
    4969 = 2*2484 + 1; hence not 2 divides 4969 by NAT_4:9;
    4969 = 3*1656 + 1; hence not 3 divides 4969 by NAT_4:9;
    4969 = 5*993 + 4; hence not 5 divides 4969 by NAT_4:9;
    4969 = 7*709 + 6; hence not 7 divides 4969 by NAT_4:9;
    4969 = 11*451 + 8; hence not 11 divides 4969 by NAT_4:9;
    4969 = 13*382 + 3; hence not 13 divides 4969 by NAT_4:9;
    4969 = 17*292 + 5; hence not 17 divides 4969 by NAT_4:9;
    4969 = 19*261 + 10; hence not 19 divides 4969 by NAT_4:9;
    4969 = 23*216 + 1; hence not 23 divides 4969 by NAT_4:9;
    4969 = 29*171 + 10; hence not 29 divides 4969 by NAT_4:9;
    4969 = 31*160 + 9; hence not 31 divides 4969 by NAT_4:9;
    4969 = 37*134 + 11; hence not 37 divides 4969 by NAT_4:9;
    4969 = 41*121 + 8; hence not 41 divides 4969 by NAT_4:9;
    4969 = 43*115 + 24; hence not 43 divides 4969 by NAT_4:9;
    4969 = 47*105 + 34; hence not 47 divides 4969 by NAT_4:9;
    4969 = 53*93 + 40; hence not 53 divides 4969 by NAT_4:9;
    4969 = 59*84 + 13; hence not 59 divides 4969 by NAT_4:9;
    4969 = 61*81 + 28; hence not 61 divides 4969 by NAT_4:9;
    4969 = 67*74 + 11; hence not 67 divides 4969 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4969 & n is prime
  holds not n divides 4969 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
