
theorem
  3607 is prime
proof
  now
    3607 = 2*1803 + 1; hence not 2 divides 3607 by NAT_4:9;
    3607 = 3*1202 + 1; hence not 3 divides 3607 by NAT_4:9;
    3607 = 5*721 + 2; hence not 5 divides 3607 by NAT_4:9;
    3607 = 7*515 + 2; hence not 7 divides 3607 by NAT_4:9;
    3607 = 11*327 + 10; hence not 11 divides 3607 by NAT_4:9;
    3607 = 13*277 + 6; hence not 13 divides 3607 by NAT_4:9;
    3607 = 17*212 + 3; hence not 17 divides 3607 by NAT_4:9;
    3607 = 19*189 + 16; hence not 19 divides 3607 by NAT_4:9;
    3607 = 23*156 + 19; hence not 23 divides 3607 by NAT_4:9;
    3607 = 29*124 + 11; hence not 29 divides 3607 by NAT_4:9;
    3607 = 31*116 + 11; hence not 31 divides 3607 by NAT_4:9;
    3607 = 37*97 + 18; hence not 37 divides 3607 by NAT_4:9;
    3607 = 41*87 + 40; hence not 41 divides 3607 by NAT_4:9;
    3607 = 43*83 + 38; hence not 43 divides 3607 by NAT_4:9;
    3607 = 47*76 + 35; hence not 47 divides 3607 by NAT_4:9;
    3607 = 53*68 + 3; hence not 53 divides 3607 by NAT_4:9;
    3607 = 59*61 + 8; hence not 59 divides 3607 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3607 & n is prime
  holds not n divides 3607 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
