
theorem
  4289 is prime
proof
  now
    4289 = 2*2144 + 1; hence not 2 divides 4289 by NAT_4:9;
    4289 = 3*1429 + 2; hence not 3 divides 4289 by NAT_4:9;
    4289 = 5*857 + 4; hence not 5 divides 4289 by NAT_4:9;
    4289 = 7*612 + 5; hence not 7 divides 4289 by NAT_4:9;
    4289 = 11*389 + 10; hence not 11 divides 4289 by NAT_4:9;
    4289 = 13*329 + 12; hence not 13 divides 4289 by NAT_4:9;
    4289 = 17*252 + 5; hence not 17 divides 4289 by NAT_4:9;
    4289 = 19*225 + 14; hence not 19 divides 4289 by NAT_4:9;
    4289 = 23*186 + 11; hence not 23 divides 4289 by NAT_4:9;
    4289 = 29*147 + 26; hence not 29 divides 4289 by NAT_4:9;
    4289 = 31*138 + 11; hence not 31 divides 4289 by NAT_4:9;
    4289 = 37*115 + 34; hence not 37 divides 4289 by NAT_4:9;
    4289 = 41*104 + 25; hence not 41 divides 4289 by NAT_4:9;
    4289 = 43*99 + 32; hence not 43 divides 4289 by NAT_4:9;
    4289 = 47*91 + 12; hence not 47 divides 4289 by NAT_4:9;
    4289 = 53*80 + 49; hence not 53 divides 4289 by NAT_4:9;
    4289 = 59*72 + 41; hence not 59 divides 4289 by NAT_4:9;
    4289 = 61*70 + 19; hence not 61 divides 4289 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4289 & n is prime
  holds not n divides 4289 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
