
theorem
  4931 is prime
proof
  now
    4931 = 2*2465 + 1; hence not 2 divides 4931 by NAT_4:9;
    4931 = 3*1643 + 2; hence not 3 divides 4931 by NAT_4:9;
    4931 = 5*986 + 1; hence not 5 divides 4931 by NAT_4:9;
    4931 = 7*704 + 3; hence not 7 divides 4931 by NAT_4:9;
    4931 = 11*448 + 3; hence not 11 divides 4931 by NAT_4:9;
    4931 = 13*379 + 4; hence not 13 divides 4931 by NAT_4:9;
    4931 = 17*290 + 1; hence not 17 divides 4931 by NAT_4:9;
    4931 = 19*259 + 10; hence not 19 divides 4931 by NAT_4:9;
    4931 = 23*214 + 9; hence not 23 divides 4931 by NAT_4:9;
    4931 = 29*170 + 1; hence not 29 divides 4931 by NAT_4:9;
    4931 = 31*159 + 2; hence not 31 divides 4931 by NAT_4:9;
    4931 = 37*133 + 10; hence not 37 divides 4931 by NAT_4:9;
    4931 = 41*120 + 11; hence not 41 divides 4931 by NAT_4:9;
    4931 = 43*114 + 29; hence not 43 divides 4931 by NAT_4:9;
    4931 = 47*104 + 43; hence not 47 divides 4931 by NAT_4:9;
    4931 = 53*93 + 2; hence not 53 divides 4931 by NAT_4:9;
    4931 = 59*83 + 34; hence not 59 divides 4931 by NAT_4:9;
    4931 = 61*80 + 51; hence not 61 divides 4931 by NAT_4:9;
    4931 = 67*73 + 40; hence not 67 divides 4931 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4931 & n is prime
  holds not n divides 4931 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
