
theorem
  4129 is prime
proof
  now
    4129 = 2*2064 + 1; hence not 2 divides 4129 by NAT_4:9;
    4129 = 3*1376 + 1; hence not 3 divides 4129 by NAT_4:9;
    4129 = 5*825 + 4; hence not 5 divides 4129 by NAT_4:9;
    4129 = 7*589 + 6; hence not 7 divides 4129 by NAT_4:9;
    4129 = 11*375 + 4; hence not 11 divides 4129 by NAT_4:9;
    4129 = 13*317 + 8; hence not 13 divides 4129 by NAT_4:9;
    4129 = 17*242 + 15; hence not 17 divides 4129 by NAT_4:9;
    4129 = 19*217 + 6; hence not 19 divides 4129 by NAT_4:9;
    4129 = 23*179 + 12; hence not 23 divides 4129 by NAT_4:9;
    4129 = 29*142 + 11; hence not 29 divides 4129 by NAT_4:9;
    4129 = 31*133 + 6; hence not 31 divides 4129 by NAT_4:9;
    4129 = 37*111 + 22; hence not 37 divides 4129 by NAT_4:9;
    4129 = 41*100 + 29; hence not 41 divides 4129 by NAT_4:9;
    4129 = 43*96 + 1; hence not 43 divides 4129 by NAT_4:9;
    4129 = 47*87 + 40; hence not 47 divides 4129 by NAT_4:9;
    4129 = 53*77 + 48; hence not 53 divides 4129 by NAT_4:9;
    4129 = 59*69 + 58; hence not 59 divides 4129 by NAT_4:9;
    4129 = 61*67 + 42; hence not 61 divides 4129 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4129 & n is prime
  holds not n divides 4129 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
