
theorem
  3617 is prime
proof
  now
    3617 = 2*1808 + 1; hence not 2 divides 3617 by NAT_4:9;
    3617 = 3*1205 + 2; hence not 3 divides 3617 by NAT_4:9;
    3617 = 5*723 + 2; hence not 5 divides 3617 by NAT_4:9;
    3617 = 7*516 + 5; hence not 7 divides 3617 by NAT_4:9;
    3617 = 11*328 + 9; hence not 11 divides 3617 by NAT_4:9;
    3617 = 13*278 + 3; hence not 13 divides 3617 by NAT_4:9;
    3617 = 17*212 + 13; hence not 17 divides 3617 by NAT_4:9;
    3617 = 19*190 + 7; hence not 19 divides 3617 by NAT_4:9;
    3617 = 23*157 + 6; hence not 23 divides 3617 by NAT_4:9;
    3617 = 29*124 + 21; hence not 29 divides 3617 by NAT_4:9;
    3617 = 31*116 + 21; hence not 31 divides 3617 by NAT_4:9;
    3617 = 37*97 + 28; hence not 37 divides 3617 by NAT_4:9;
    3617 = 41*88 + 9; hence not 41 divides 3617 by NAT_4:9;
    3617 = 43*84 + 5; hence not 43 divides 3617 by NAT_4:9;
    3617 = 47*76 + 45; hence not 47 divides 3617 by NAT_4:9;
    3617 = 53*68 + 13; hence not 53 divides 3617 by NAT_4:9;
    3617 = 59*61 + 18; hence not 59 divides 3617 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3617 & n is prime
  holds not n divides 3617 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
