
theorem
  4261 is prime
proof
  now
    4261 = 2*2130 + 1; hence not 2 divides 4261 by NAT_4:9;
    4261 = 3*1420 + 1; hence not 3 divides 4261 by NAT_4:9;
    4261 = 5*852 + 1; hence not 5 divides 4261 by NAT_4:9;
    4261 = 7*608 + 5; hence not 7 divides 4261 by NAT_4:9;
    4261 = 11*387 + 4; hence not 11 divides 4261 by NAT_4:9;
    4261 = 13*327 + 10; hence not 13 divides 4261 by NAT_4:9;
    4261 = 17*250 + 11; hence not 17 divides 4261 by NAT_4:9;
    4261 = 19*224 + 5; hence not 19 divides 4261 by NAT_4:9;
    4261 = 23*185 + 6; hence not 23 divides 4261 by NAT_4:9;
    4261 = 29*146 + 27; hence not 29 divides 4261 by NAT_4:9;
    4261 = 31*137 + 14; hence not 31 divides 4261 by NAT_4:9;
    4261 = 37*115 + 6; hence not 37 divides 4261 by NAT_4:9;
    4261 = 41*103 + 38; hence not 41 divides 4261 by NAT_4:9;
    4261 = 43*99 + 4; hence not 43 divides 4261 by NAT_4:9;
    4261 = 47*90 + 31; hence not 47 divides 4261 by NAT_4:9;
    4261 = 53*80 + 21; hence not 53 divides 4261 by NAT_4:9;
    4261 = 59*72 + 13; hence not 59 divides 4261 by NAT_4:9;
    4261 = 61*69 + 52; hence not 61 divides 4261 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4261 & n is prime
  holds not n divides 4261 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
