
theorem
  3571 is prime
proof
  now
    3571 = 2*1785 + 1; hence not 2 divides 3571 by NAT_4:9;
    3571 = 3*1190 + 1; hence not 3 divides 3571 by NAT_4:9;
    3571 = 5*714 + 1; hence not 5 divides 3571 by NAT_4:9;
    3571 = 7*510 + 1; hence not 7 divides 3571 by NAT_4:9;
    3571 = 11*324 + 7; hence not 11 divides 3571 by NAT_4:9;
    3571 = 13*274 + 9; hence not 13 divides 3571 by NAT_4:9;
    3571 = 17*210 + 1; hence not 17 divides 3571 by NAT_4:9;
    3571 = 19*187 + 18; hence not 19 divides 3571 by NAT_4:9;
    3571 = 23*155 + 6; hence not 23 divides 3571 by NAT_4:9;
    3571 = 29*123 + 4; hence not 29 divides 3571 by NAT_4:9;
    3571 = 31*115 + 6; hence not 31 divides 3571 by NAT_4:9;
    3571 = 37*96 + 19; hence not 37 divides 3571 by NAT_4:9;
    3571 = 41*87 + 4; hence not 41 divides 3571 by NAT_4:9;
    3571 = 43*83 + 2; hence not 43 divides 3571 by NAT_4:9;
    3571 = 47*75 + 46; hence not 47 divides 3571 by NAT_4:9;
    3571 = 53*67 + 20; hence not 53 divides 3571 by NAT_4:9;
    3571 = 59*60 + 31; hence not 59 divides 3571 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3571 & n is prime
  holds not n divides 3571 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
