
theorem
  5021 is prime
proof
  now
    5021 = 2*2510 + 1; hence not 2 divides 5021 by NAT_4:9;
    5021 = 3*1673 + 2; hence not 3 divides 5021 by NAT_4:9;
    5021 = 5*1004 + 1; hence not 5 divides 5021 by NAT_4:9;
    5021 = 7*717 + 2; hence not 7 divides 5021 by NAT_4:9;
    5021 = 11*456 + 5; hence not 11 divides 5021 by NAT_4:9;
    5021 = 13*386 + 3; hence not 13 divides 5021 by NAT_4:9;
    5021 = 17*295 + 6; hence not 17 divides 5021 by NAT_4:9;
    5021 = 19*264 + 5; hence not 19 divides 5021 by NAT_4:9;
    5021 = 23*218 + 7; hence not 23 divides 5021 by NAT_4:9;
    5021 = 29*173 + 4; hence not 29 divides 5021 by NAT_4:9;
    5021 = 31*161 + 30; hence not 31 divides 5021 by NAT_4:9;
    5021 = 37*135 + 26; hence not 37 divides 5021 by NAT_4:9;
    5021 = 41*122 + 19; hence not 41 divides 5021 by NAT_4:9;
    5021 = 43*116 + 33; hence not 43 divides 5021 by NAT_4:9;
    5021 = 47*106 + 39; hence not 47 divides 5021 by NAT_4:9;
    5021 = 53*94 + 39; hence not 53 divides 5021 by NAT_4:9;
    5021 = 59*85 + 6; hence not 59 divides 5021 by NAT_4:9;
    5021 = 61*82 + 19; hence not 61 divides 5021 by NAT_4:9;
    5021 = 67*74 + 63; hence not 67 divides 5021 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5021 & n is prime
  holds not n divides 5021 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
