
theorem
  5099 is prime
proof
  now
    5099 = 2*2549 + 1; hence not 2 divides 5099 by NAT_4:9;
    5099 = 3*1699 + 2; hence not 3 divides 5099 by NAT_4:9;
    5099 = 5*1019 + 4; hence not 5 divides 5099 by NAT_4:9;
    5099 = 7*728 + 3; hence not 7 divides 5099 by NAT_4:9;
    5099 = 11*463 + 6; hence not 11 divides 5099 by NAT_4:9;
    5099 = 13*392 + 3; hence not 13 divides 5099 by NAT_4:9;
    5099 = 17*299 + 16; hence not 17 divides 5099 by NAT_4:9;
    5099 = 19*268 + 7; hence not 19 divides 5099 by NAT_4:9;
    5099 = 23*221 + 16; hence not 23 divides 5099 by NAT_4:9;
    5099 = 29*175 + 24; hence not 29 divides 5099 by NAT_4:9;
    5099 = 31*164 + 15; hence not 31 divides 5099 by NAT_4:9;
    5099 = 37*137 + 30; hence not 37 divides 5099 by NAT_4:9;
    5099 = 41*124 + 15; hence not 41 divides 5099 by NAT_4:9;
    5099 = 43*118 + 25; hence not 43 divides 5099 by NAT_4:9;
    5099 = 47*108 + 23; hence not 47 divides 5099 by NAT_4:9;
    5099 = 53*96 + 11; hence not 53 divides 5099 by NAT_4:9;
    5099 = 59*86 + 25; hence not 59 divides 5099 by NAT_4:9;
    5099 = 61*83 + 36; hence not 61 divides 5099 by NAT_4:9;
    5099 = 67*76 + 7; hence not 67 divides 5099 by NAT_4:9;
    5099 = 71*71 + 58; hence not 71 divides 5099 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5099 & n is prime
  holds not n divides 5099 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
