
theorem
  4861 is prime
proof
  now
    4861 = 2*2430 + 1; hence not 2 divides 4861 by NAT_4:9;
    4861 = 3*1620 + 1; hence not 3 divides 4861 by NAT_4:9;
    4861 = 5*972 + 1; hence not 5 divides 4861 by NAT_4:9;
    4861 = 7*694 + 3; hence not 7 divides 4861 by NAT_4:9;
    4861 = 11*441 + 10; hence not 11 divides 4861 by NAT_4:9;
    4861 = 13*373 + 12; hence not 13 divides 4861 by NAT_4:9;
    4861 = 17*285 + 16; hence not 17 divides 4861 by NAT_4:9;
    4861 = 19*255 + 16; hence not 19 divides 4861 by NAT_4:9;
    4861 = 23*211 + 8; hence not 23 divides 4861 by NAT_4:9;
    4861 = 29*167 + 18; hence not 29 divides 4861 by NAT_4:9;
    4861 = 31*156 + 25; hence not 31 divides 4861 by NAT_4:9;
    4861 = 37*131 + 14; hence not 37 divides 4861 by NAT_4:9;
    4861 = 41*118 + 23; hence not 41 divides 4861 by NAT_4:9;
    4861 = 43*113 + 2; hence not 43 divides 4861 by NAT_4:9;
    4861 = 47*103 + 20; hence not 47 divides 4861 by NAT_4:9;
    4861 = 53*91 + 38; hence not 53 divides 4861 by NAT_4:9;
    4861 = 59*82 + 23; hence not 59 divides 4861 by NAT_4:9;
    4861 = 61*79 + 42; hence not 61 divides 4861 by NAT_4:9;
    4861 = 67*72 + 37; hence not 67 divides 4861 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4861 & n is prime
  holds not n divides 4861 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
