
theorem
  2617 is prime
proof
  now
    2617 = 2*1308 + 1; hence not 2 divides 2617 by NAT_4:9;
    2617 = 3*872 + 1; hence not 3 divides 2617 by NAT_4:9;
    2617 = 5*523 + 2; hence not 5 divides 2617 by NAT_4:9;
    2617 = 7*373 + 6; hence not 7 divides 2617 by NAT_4:9;
    2617 = 11*237 + 10; hence not 11 divides 2617 by NAT_4:9;
    2617 = 13*201 + 4; hence not 13 divides 2617 by NAT_4:9;
    2617 = 17*153 + 16; hence not 17 divides 2617 by NAT_4:9;
    2617 = 19*137 + 14; hence not 19 divides 2617 by NAT_4:9;
    2617 = 23*113 + 18; hence not 23 divides 2617 by NAT_4:9;
    2617 = 29*90 + 7; hence not 29 divides 2617 by NAT_4:9;
    2617 = 31*84 + 13; hence not 31 divides 2617 by NAT_4:9;
    2617 = 37*70 + 27; hence not 37 divides 2617 by NAT_4:9;
    2617 = 41*63 + 34; hence not 41 divides 2617 by NAT_4:9;
    2617 = 43*60 + 37; hence not 43 divides 2617 by NAT_4:9;
    2617 = 47*55 + 32; hence not 47 divides 2617 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2617 & n is prime
  holds not n divides 2617 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
