
theorem
  5261 is prime
proof
  now
    5261 = 2*2630 + 1; hence not 2 divides 5261 by NAT_4:9;
    5261 = 3*1753 + 2; hence not 3 divides 5261 by NAT_4:9;
    5261 = 5*1052 + 1; hence not 5 divides 5261 by NAT_4:9;
    5261 = 7*751 + 4; hence not 7 divides 5261 by NAT_4:9;
    5261 = 11*478 + 3; hence not 11 divides 5261 by NAT_4:9;
    5261 = 13*404 + 9; hence not 13 divides 5261 by NAT_4:9;
    5261 = 17*309 + 8; hence not 17 divides 5261 by NAT_4:9;
    5261 = 19*276 + 17; hence not 19 divides 5261 by NAT_4:9;
    5261 = 23*228 + 17; hence not 23 divides 5261 by NAT_4:9;
    5261 = 29*181 + 12; hence not 29 divides 5261 by NAT_4:9;
    5261 = 31*169 + 22; hence not 31 divides 5261 by NAT_4:9;
    5261 = 37*142 + 7; hence not 37 divides 5261 by NAT_4:9;
    5261 = 41*128 + 13; hence not 41 divides 5261 by NAT_4:9;
    5261 = 43*122 + 15; hence not 43 divides 5261 by NAT_4:9;
    5261 = 47*111 + 44; hence not 47 divides 5261 by NAT_4:9;
    5261 = 53*99 + 14; hence not 53 divides 5261 by NAT_4:9;
    5261 = 59*89 + 10; hence not 59 divides 5261 by NAT_4:9;
    5261 = 61*86 + 15; hence not 61 divides 5261 by NAT_4:9;
    5261 = 67*78 + 35; hence not 67 divides 5261 by NAT_4:9;
    5261 = 71*74 + 7; hence not 71 divides 5261 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5261 & n is prime
  holds not n divides 5261 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
