
theorem
  3691 is prime
proof
  now
    3691 = 2*1845 + 1; hence not 2 divides 3691 by NAT_4:9;
    3691 = 3*1230 + 1; hence not 3 divides 3691 by NAT_4:9;
    3691 = 5*738 + 1; hence not 5 divides 3691 by NAT_4:9;
    3691 = 7*527 + 2; hence not 7 divides 3691 by NAT_4:9;
    3691 = 11*335 + 6; hence not 11 divides 3691 by NAT_4:9;
    3691 = 13*283 + 12; hence not 13 divides 3691 by NAT_4:9;
    3691 = 17*217 + 2; hence not 17 divides 3691 by NAT_4:9;
    3691 = 19*194 + 5; hence not 19 divides 3691 by NAT_4:9;
    3691 = 23*160 + 11; hence not 23 divides 3691 by NAT_4:9;
    3691 = 29*127 + 8; hence not 29 divides 3691 by NAT_4:9;
    3691 = 31*119 + 2; hence not 31 divides 3691 by NAT_4:9;
    3691 = 37*99 + 28; hence not 37 divides 3691 by NAT_4:9;
    3691 = 41*90 + 1; hence not 41 divides 3691 by NAT_4:9;
    3691 = 43*85 + 36; hence not 43 divides 3691 by NAT_4:9;
    3691 = 47*78 + 25; hence not 47 divides 3691 by NAT_4:9;
    3691 = 53*69 + 34; hence not 53 divides 3691 by NAT_4:9;
    3691 = 59*62 + 33; hence not 59 divides 3691 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3691 & n is prime
  holds not n divides 3691 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
