
theorem
  4937 is prime
proof
  now
    4937 = 2*2468 + 1; hence not 2 divides 4937 by NAT_4:9;
    4937 = 3*1645 + 2; hence not 3 divides 4937 by NAT_4:9;
    4937 = 5*987 + 2; hence not 5 divides 4937 by NAT_4:9;
    4937 = 7*705 + 2; hence not 7 divides 4937 by NAT_4:9;
    4937 = 11*448 + 9; hence not 11 divides 4937 by NAT_4:9;
    4937 = 13*379 + 10; hence not 13 divides 4937 by NAT_4:9;
    4937 = 17*290 + 7; hence not 17 divides 4937 by NAT_4:9;
    4937 = 19*259 + 16; hence not 19 divides 4937 by NAT_4:9;
    4937 = 23*214 + 15; hence not 23 divides 4937 by NAT_4:9;
    4937 = 29*170 + 7; hence not 29 divides 4937 by NAT_4:9;
    4937 = 31*159 + 8; hence not 31 divides 4937 by NAT_4:9;
    4937 = 37*133 + 16; hence not 37 divides 4937 by NAT_4:9;
    4937 = 41*120 + 17; hence not 41 divides 4937 by NAT_4:9;
    4937 = 43*114 + 35; hence not 43 divides 4937 by NAT_4:9;
    4937 = 47*105 + 2; hence not 47 divides 4937 by NAT_4:9;
    4937 = 53*93 + 8; hence not 53 divides 4937 by NAT_4:9;
    4937 = 59*83 + 40; hence not 59 divides 4937 by NAT_4:9;
    4937 = 61*80 + 57; hence not 61 divides 4937 by NAT_4:9;
    4937 = 67*73 + 46; hence not 67 divides 4937 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4937 & n is prime
  holds not n divides 4937 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
