
theorem
  4957 is prime
proof
  now
    4957 = 2*2478 + 1; hence not 2 divides 4957 by NAT_4:9;
    4957 = 3*1652 + 1; hence not 3 divides 4957 by NAT_4:9;
    4957 = 5*991 + 2; hence not 5 divides 4957 by NAT_4:9;
    4957 = 7*708 + 1; hence not 7 divides 4957 by NAT_4:9;
    4957 = 11*450 + 7; hence not 11 divides 4957 by NAT_4:9;
    4957 = 13*381 + 4; hence not 13 divides 4957 by NAT_4:9;
    4957 = 17*291 + 10; hence not 17 divides 4957 by NAT_4:9;
    4957 = 19*260 + 17; hence not 19 divides 4957 by NAT_4:9;
    4957 = 23*215 + 12; hence not 23 divides 4957 by NAT_4:9;
    4957 = 29*170 + 27; hence not 29 divides 4957 by NAT_4:9;
    4957 = 31*159 + 28; hence not 31 divides 4957 by NAT_4:9;
    4957 = 37*133 + 36; hence not 37 divides 4957 by NAT_4:9;
    4957 = 41*120 + 37; hence not 41 divides 4957 by NAT_4:9;
    4957 = 43*115 + 12; hence not 43 divides 4957 by NAT_4:9;
    4957 = 47*105 + 22; hence not 47 divides 4957 by NAT_4:9;
    4957 = 53*93 + 28; hence not 53 divides 4957 by NAT_4:9;
    4957 = 59*84 + 1; hence not 59 divides 4957 by NAT_4:9;
    4957 = 61*81 + 16; hence not 61 divides 4957 by NAT_4:9;
    4957 = 67*73 + 66; hence not 67 divides 4957 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4957 & n is prime
  holds not n divides 4957 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
