
theorem
  3701 is prime
proof
  now
    3701 = 2*1850 + 1; hence not 2 divides 3701 by NAT_4:9;
    3701 = 3*1233 + 2; hence not 3 divides 3701 by NAT_4:9;
    3701 = 5*740 + 1; hence not 5 divides 3701 by NAT_4:9;
    3701 = 7*528 + 5; hence not 7 divides 3701 by NAT_4:9;
    3701 = 11*336 + 5; hence not 11 divides 3701 by NAT_4:9;
    3701 = 13*284 + 9; hence not 13 divides 3701 by NAT_4:9;
    3701 = 17*217 + 12; hence not 17 divides 3701 by NAT_4:9;
    3701 = 19*194 + 15; hence not 19 divides 3701 by NAT_4:9;
    3701 = 23*160 + 21; hence not 23 divides 3701 by NAT_4:9;
    3701 = 29*127 + 18; hence not 29 divides 3701 by NAT_4:9;
    3701 = 31*119 + 12; hence not 31 divides 3701 by NAT_4:9;
    3701 = 37*100 + 1; hence not 37 divides 3701 by NAT_4:9;
    3701 = 41*90 + 11; hence not 41 divides 3701 by NAT_4:9;
    3701 = 43*86 + 3; hence not 43 divides 3701 by NAT_4:9;
    3701 = 47*78 + 35; hence not 47 divides 3701 by NAT_4:9;
    3701 = 53*69 + 44; hence not 53 divides 3701 by NAT_4:9;
    3701 = 59*62 + 43; hence not 59 divides 3701 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3701 & n is prime
  holds not n divides 3701 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
