
theorem
  2963 is prime
proof
  now
    2963 = 2*1481 + 1; hence not 2 divides 2963 by NAT_4:9;
    2963 = 3*987 + 2; hence not 3 divides 2963 by NAT_4:9;
    2963 = 5*592 + 3; hence not 5 divides 2963 by NAT_4:9;
    2963 = 7*423 + 2; hence not 7 divides 2963 by NAT_4:9;
    2963 = 11*269 + 4; hence not 11 divides 2963 by NAT_4:9;
    2963 = 13*227 + 12; hence not 13 divides 2963 by NAT_4:9;
    2963 = 17*174 + 5; hence not 17 divides 2963 by NAT_4:9;
    2963 = 19*155 + 18; hence not 19 divides 2963 by NAT_4:9;
    2963 = 23*128 + 19; hence not 23 divides 2963 by NAT_4:9;
    2963 = 29*102 + 5; hence not 29 divides 2963 by NAT_4:9;
    2963 = 31*95 + 18; hence not 31 divides 2963 by NAT_4:9;
    2963 = 37*80 + 3; hence not 37 divides 2963 by NAT_4:9;
    2963 = 41*72 + 11; hence not 41 divides 2963 by NAT_4:9;
    2963 = 43*68 + 39; hence not 43 divides 2963 by NAT_4:9;
    2963 = 47*63 + 2; hence not 47 divides 2963 by NAT_4:9;
    2963 = 53*55 + 48; hence not 53 divides 2963 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2963 & n is prime
  holds not n divides 2963 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
