
theorem
  3019 is prime
proof
  now
    3019 = 2*1509 + 1; hence not 2 divides 3019 by NAT_4:9;
    3019 = 3*1006 + 1; hence not 3 divides 3019 by NAT_4:9;
    3019 = 5*603 + 4; hence not 5 divides 3019 by NAT_4:9;
    3019 = 7*431 + 2; hence not 7 divides 3019 by NAT_4:9;
    3019 = 11*274 + 5; hence not 11 divides 3019 by NAT_4:9;
    3019 = 13*232 + 3; hence not 13 divides 3019 by NAT_4:9;
    3019 = 17*177 + 10; hence not 17 divides 3019 by NAT_4:9;
    3019 = 19*158 + 17; hence not 19 divides 3019 by NAT_4:9;
    3019 = 23*131 + 6; hence not 23 divides 3019 by NAT_4:9;
    3019 = 29*104 + 3; hence not 29 divides 3019 by NAT_4:9;
    3019 = 31*97 + 12; hence not 31 divides 3019 by NAT_4:9;
    3019 = 37*81 + 22; hence not 37 divides 3019 by NAT_4:9;
    3019 = 41*73 + 26; hence not 41 divides 3019 by NAT_4:9;
    3019 = 43*70 + 9; hence not 43 divides 3019 by NAT_4:9;
    3019 = 47*64 + 11; hence not 47 divides 3019 by NAT_4:9;
    3019 = 53*56 + 51; hence not 53 divides 3019 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3019 & n is prime
  holds not n divides 3019 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
