
theorem
  3061 is prime
proof
  now
    3061 = 2*1530 + 1; hence not 2 divides 3061 by NAT_4:9;
    3061 = 3*1020 + 1; hence not 3 divides 3061 by NAT_4:9;
    3061 = 5*612 + 1; hence not 5 divides 3061 by NAT_4:9;
    3061 = 7*437 + 2; hence not 7 divides 3061 by NAT_4:9;
    3061 = 11*278 + 3; hence not 11 divides 3061 by NAT_4:9;
    3061 = 13*235 + 6; hence not 13 divides 3061 by NAT_4:9;
    3061 = 17*180 + 1; hence not 17 divides 3061 by NAT_4:9;
    3061 = 19*161 + 2; hence not 19 divides 3061 by NAT_4:9;
    3061 = 23*133 + 2; hence not 23 divides 3061 by NAT_4:9;
    3061 = 29*105 + 16; hence not 29 divides 3061 by NAT_4:9;
    3061 = 31*98 + 23; hence not 31 divides 3061 by NAT_4:9;
    3061 = 37*82 + 27; hence not 37 divides 3061 by NAT_4:9;
    3061 = 41*74 + 27; hence not 41 divides 3061 by NAT_4:9;
    3061 = 43*71 + 8; hence not 43 divides 3061 by NAT_4:9;
    3061 = 47*65 + 6; hence not 47 divides 3061 by NAT_4:9;
    3061 = 53*57 + 40; hence not 53 divides 3061 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3061 & n is prime
  holds not n divides 3061 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
