
theorem
  3541 is prime
proof
  now
    3541 = 2*1770 + 1; hence not 2 divides 3541 by NAT_4:9;
    3541 = 3*1180 + 1; hence not 3 divides 3541 by NAT_4:9;
    3541 = 5*708 + 1; hence not 5 divides 3541 by NAT_4:9;
    3541 = 7*505 + 6; hence not 7 divides 3541 by NAT_4:9;
    3541 = 11*321 + 10; hence not 11 divides 3541 by NAT_4:9;
    3541 = 13*272 + 5; hence not 13 divides 3541 by NAT_4:9;
    3541 = 17*208 + 5; hence not 17 divides 3541 by NAT_4:9;
    3541 = 19*186 + 7; hence not 19 divides 3541 by NAT_4:9;
    3541 = 23*153 + 22; hence not 23 divides 3541 by NAT_4:9;
    3541 = 29*122 + 3; hence not 29 divides 3541 by NAT_4:9;
    3541 = 31*114 + 7; hence not 31 divides 3541 by NAT_4:9;
    3541 = 37*95 + 26; hence not 37 divides 3541 by NAT_4:9;
    3541 = 41*86 + 15; hence not 41 divides 3541 by NAT_4:9;
    3541 = 43*82 + 15; hence not 43 divides 3541 by NAT_4:9;
    3541 = 47*75 + 16; hence not 47 divides 3541 by NAT_4:9;
    3541 = 53*66 + 43; hence not 53 divides 3541 by NAT_4:9;
    3541 = 59*60 + 1; hence not 59 divides 3541 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3541 & n is prime
  holds not n divides 3541 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
