
theorem
  3547 is prime
proof
  now
    3547 = 2*1773 + 1; hence not 2 divides 3547 by NAT_4:9;
    3547 = 3*1182 + 1; hence not 3 divides 3547 by NAT_4:9;
    3547 = 5*709 + 2; hence not 5 divides 3547 by NAT_4:9;
    3547 = 7*506 + 5; hence not 7 divides 3547 by NAT_4:9;
    3547 = 11*322 + 5; hence not 11 divides 3547 by NAT_4:9;
    3547 = 13*272 + 11; hence not 13 divides 3547 by NAT_4:9;
    3547 = 17*208 + 11; hence not 17 divides 3547 by NAT_4:9;
    3547 = 19*186 + 13; hence not 19 divides 3547 by NAT_4:9;
    3547 = 23*154 + 5; hence not 23 divides 3547 by NAT_4:9;
    3547 = 29*122 + 9; hence not 29 divides 3547 by NAT_4:9;
    3547 = 31*114 + 13; hence not 31 divides 3547 by NAT_4:9;
    3547 = 37*95 + 32; hence not 37 divides 3547 by NAT_4:9;
    3547 = 41*86 + 21; hence not 41 divides 3547 by NAT_4:9;
    3547 = 43*82 + 21; hence not 43 divides 3547 by NAT_4:9;
    3547 = 47*75 + 22; hence not 47 divides 3547 by NAT_4:9;
    3547 = 53*66 + 49; hence not 53 divides 3547 by NAT_4:9;
    3547 = 59*60 + 7; hence not 59 divides 3547 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3547 & n is prime
  holds not n divides 3547 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
