
theorem
  3527 is prime
proof
  now
    3527 = 2*1763 + 1; hence not 2 divides 3527 by NAT_4:9;
    3527 = 3*1175 + 2; hence not 3 divides 3527 by NAT_4:9;
    3527 = 5*705 + 2; hence not 5 divides 3527 by NAT_4:9;
    3527 = 7*503 + 6; hence not 7 divides 3527 by NAT_4:9;
    3527 = 11*320 + 7; hence not 11 divides 3527 by NAT_4:9;
    3527 = 13*271 + 4; hence not 13 divides 3527 by NAT_4:9;
    3527 = 17*207 + 8; hence not 17 divides 3527 by NAT_4:9;
    3527 = 19*185 + 12; hence not 19 divides 3527 by NAT_4:9;
    3527 = 23*153 + 8; hence not 23 divides 3527 by NAT_4:9;
    3527 = 29*121 + 18; hence not 29 divides 3527 by NAT_4:9;
    3527 = 31*113 + 24; hence not 31 divides 3527 by NAT_4:9;
    3527 = 37*95 + 12; hence not 37 divides 3527 by NAT_4:9;
    3527 = 41*86 + 1; hence not 41 divides 3527 by NAT_4:9;
    3527 = 43*82 + 1; hence not 43 divides 3527 by NAT_4:9;
    3527 = 47*75 + 2; hence not 47 divides 3527 by NAT_4:9;
    3527 = 53*66 + 29; hence not 53 divides 3527 by NAT_4:9;
    3527 = 59*59 + 46; hence not 59 divides 3527 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3527 & n is prime
  holds not n divides 3527 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
