
theorem
  4987 is prime
proof
  now
    4987 = 2*2493 + 1; hence not 2 divides 4987 by NAT_4:9;
    4987 = 3*1662 + 1; hence not 3 divides 4987 by NAT_4:9;
    4987 = 5*997 + 2; hence not 5 divides 4987 by NAT_4:9;
    4987 = 7*712 + 3; hence not 7 divides 4987 by NAT_4:9;
    4987 = 11*453 + 4; hence not 11 divides 4987 by NAT_4:9;
    4987 = 13*383 + 8; hence not 13 divides 4987 by NAT_4:9;
    4987 = 17*293 + 6; hence not 17 divides 4987 by NAT_4:9;
    4987 = 19*262 + 9; hence not 19 divides 4987 by NAT_4:9;
    4987 = 23*216 + 19; hence not 23 divides 4987 by NAT_4:9;
    4987 = 29*171 + 28; hence not 29 divides 4987 by NAT_4:9;
    4987 = 31*160 + 27; hence not 31 divides 4987 by NAT_4:9;
    4987 = 37*134 + 29; hence not 37 divides 4987 by NAT_4:9;
    4987 = 41*121 + 26; hence not 41 divides 4987 by NAT_4:9;
    4987 = 43*115 + 42; hence not 43 divides 4987 by NAT_4:9;
    4987 = 47*106 + 5; hence not 47 divides 4987 by NAT_4:9;
    4987 = 53*94 + 5; hence not 53 divides 4987 by NAT_4:9;
    4987 = 59*84 + 31; hence not 59 divides 4987 by NAT_4:9;
    4987 = 61*81 + 46; hence not 61 divides 4987 by NAT_4:9;
    4987 = 67*74 + 29; hence not 67 divides 4987 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4987 & n is prime
  holds not n divides 4987 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
