
theorem
  4691 is prime
proof
  now
    4691 = 2*2345 + 1; hence not 2 divides 4691 by NAT_4:9;
    4691 = 3*1563 + 2; hence not 3 divides 4691 by NAT_4:9;
    4691 = 5*938 + 1; hence not 5 divides 4691 by NAT_4:9;
    4691 = 7*670 + 1; hence not 7 divides 4691 by NAT_4:9;
    4691 = 11*426 + 5; hence not 11 divides 4691 by NAT_4:9;
    4691 = 13*360 + 11; hence not 13 divides 4691 by NAT_4:9;
    4691 = 17*275 + 16; hence not 17 divides 4691 by NAT_4:9;
    4691 = 19*246 + 17; hence not 19 divides 4691 by NAT_4:9;
    4691 = 23*203 + 22; hence not 23 divides 4691 by NAT_4:9;
    4691 = 29*161 + 22; hence not 29 divides 4691 by NAT_4:9;
    4691 = 31*151 + 10; hence not 31 divides 4691 by NAT_4:9;
    4691 = 37*126 + 29; hence not 37 divides 4691 by NAT_4:9;
    4691 = 41*114 + 17; hence not 41 divides 4691 by NAT_4:9;
    4691 = 43*109 + 4; hence not 43 divides 4691 by NAT_4:9;
    4691 = 47*99 + 38; hence not 47 divides 4691 by NAT_4:9;
    4691 = 53*88 + 27; hence not 53 divides 4691 by NAT_4:9;
    4691 = 59*79 + 30; hence not 59 divides 4691 by NAT_4:9;
    4691 = 61*76 + 55; hence not 61 divides 4691 by NAT_4:9;
    4691 = 67*70 + 1; hence not 67 divides 4691 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4691 & n is prime
  holds not n divides 4691 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
