
theorem
  4729 is prime
proof
  now
    4729 = 2*2364 + 1; hence not 2 divides 4729 by NAT_4:9;
    4729 = 3*1576 + 1; hence not 3 divides 4729 by NAT_4:9;
    4729 = 5*945 + 4; hence not 5 divides 4729 by NAT_4:9;
    4729 = 7*675 + 4; hence not 7 divides 4729 by NAT_4:9;
    4729 = 11*429 + 10; hence not 11 divides 4729 by NAT_4:9;
    4729 = 13*363 + 10; hence not 13 divides 4729 by NAT_4:9;
    4729 = 17*278 + 3; hence not 17 divides 4729 by NAT_4:9;
    4729 = 19*248 + 17; hence not 19 divides 4729 by NAT_4:9;
    4729 = 23*205 + 14; hence not 23 divides 4729 by NAT_4:9;
    4729 = 29*163 + 2; hence not 29 divides 4729 by NAT_4:9;
    4729 = 31*152 + 17; hence not 31 divides 4729 by NAT_4:9;
    4729 = 37*127 + 30; hence not 37 divides 4729 by NAT_4:9;
    4729 = 41*115 + 14; hence not 41 divides 4729 by NAT_4:9;
    4729 = 43*109 + 42; hence not 43 divides 4729 by NAT_4:9;
    4729 = 47*100 + 29; hence not 47 divides 4729 by NAT_4:9;
    4729 = 53*89 + 12; hence not 53 divides 4729 by NAT_4:9;
    4729 = 59*80 + 9; hence not 59 divides 4729 by NAT_4:9;
    4729 = 61*77 + 32; hence not 61 divides 4729 by NAT_4:9;
    4729 = 67*70 + 39; hence not 67 divides 4729 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4729 & n is prime
  holds not n divides 4729 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
