
theorem
  5077 is prime
proof
  now
    5077 = 2*2538 + 1; hence not 2 divides 5077 by NAT_4:9;
    5077 = 3*1692 + 1; hence not 3 divides 5077 by NAT_4:9;
    5077 = 5*1015 + 2; hence not 5 divides 5077 by NAT_4:9;
    5077 = 7*725 + 2; hence not 7 divides 5077 by NAT_4:9;
    5077 = 11*461 + 6; hence not 11 divides 5077 by NAT_4:9;
    5077 = 13*390 + 7; hence not 13 divides 5077 by NAT_4:9;
    5077 = 17*298 + 11; hence not 17 divides 5077 by NAT_4:9;
    5077 = 19*267 + 4; hence not 19 divides 5077 by NAT_4:9;
    5077 = 23*220 + 17; hence not 23 divides 5077 by NAT_4:9;
    5077 = 29*175 + 2; hence not 29 divides 5077 by NAT_4:9;
    5077 = 31*163 + 24; hence not 31 divides 5077 by NAT_4:9;
    5077 = 37*137 + 8; hence not 37 divides 5077 by NAT_4:9;
    5077 = 41*123 + 34; hence not 41 divides 5077 by NAT_4:9;
    5077 = 43*118 + 3; hence not 43 divides 5077 by NAT_4:9;
    5077 = 47*108 + 1; hence not 47 divides 5077 by NAT_4:9;
    5077 = 53*95 + 42; hence not 53 divides 5077 by NAT_4:9;
    5077 = 59*86 + 3; hence not 59 divides 5077 by NAT_4:9;
    5077 = 61*83 + 14; hence not 61 divides 5077 by NAT_4:9;
    5077 = 67*75 + 52; hence not 67 divides 5077 by NAT_4:9;
    5077 = 71*71 + 36; hence not 71 divides 5077 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5077 & n is prime
  holds not n divides 5077 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
