
theorem
  3709 is prime
proof
  now
    3709 = 2*1854 + 1; hence not 2 divides 3709 by NAT_4:9;
    3709 = 3*1236 + 1; hence not 3 divides 3709 by NAT_4:9;
    3709 = 5*741 + 4; hence not 5 divides 3709 by NAT_4:9;
    3709 = 7*529 + 6; hence not 7 divides 3709 by NAT_4:9;
    3709 = 11*337 + 2; hence not 11 divides 3709 by NAT_4:9;
    3709 = 13*285 + 4; hence not 13 divides 3709 by NAT_4:9;
    3709 = 17*218 + 3; hence not 17 divides 3709 by NAT_4:9;
    3709 = 19*195 + 4; hence not 19 divides 3709 by NAT_4:9;
    3709 = 23*161 + 6; hence not 23 divides 3709 by NAT_4:9;
    3709 = 29*127 + 26; hence not 29 divides 3709 by NAT_4:9;
    3709 = 31*119 + 20; hence not 31 divides 3709 by NAT_4:9;
    3709 = 37*100 + 9; hence not 37 divides 3709 by NAT_4:9;
    3709 = 41*90 + 19; hence not 41 divides 3709 by NAT_4:9;
    3709 = 43*86 + 11; hence not 43 divides 3709 by NAT_4:9;
    3709 = 47*78 + 43; hence not 47 divides 3709 by NAT_4:9;
    3709 = 53*69 + 52; hence not 53 divides 3709 by NAT_4:9;
    3709 = 59*62 + 51; hence not 59 divides 3709 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3709 & n is prime
  holds not n divides 3709 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
