
theorem
  7159 is prime
proof
  now
    7159 = 2*3579 + 1; hence not 2 divides 7159 by NAT_4:9;
    7159 = 3*2386 + 1; hence not 3 divides 7159 by NAT_4:9;
    7159 = 5*1431 + 4; hence not 5 divides 7159 by NAT_4:9;
    7159 = 7*1022 + 5; hence not 7 divides 7159 by NAT_4:9;
    7159 = 11*650 + 9; hence not 11 divides 7159 by NAT_4:9;
    7159 = 13*550 + 9; hence not 13 divides 7159 by NAT_4:9;
    7159 = 17*421 + 2; hence not 17 divides 7159 by NAT_4:9;
    7159 = 19*376 + 15; hence not 19 divides 7159 by NAT_4:9;
    7159 = 23*311 + 6; hence not 23 divides 7159 by NAT_4:9;
    7159 = 29*246 + 25; hence not 29 divides 7159 by NAT_4:9;
    7159 = 31*230 + 29; hence not 31 divides 7159 by NAT_4:9;
    7159 = 37*193 + 18; hence not 37 divides 7159 by NAT_4:9;
    7159 = 41*174 + 25; hence not 41 divides 7159 by NAT_4:9;
    7159 = 43*166 + 21; hence not 43 divides 7159 by NAT_4:9;
    7159 = 47*152 + 15; hence not 47 divides 7159 by NAT_4:9;
    7159 = 53*135 + 4; hence not 53 divides 7159 by NAT_4:9;
    7159 = 59*121 + 20; hence not 59 divides 7159 by NAT_4:9;
    7159 = 61*117 + 22; hence not 61 divides 7159 by NAT_4:9;
    7159 = 67*106 + 57; hence not 67 divides 7159 by NAT_4:9;
    7159 = 71*100 + 59; hence not 71 divides 7159 by NAT_4:9;
    7159 = 73*98 + 5; hence not 73 divides 7159 by NAT_4:9;
    7159 = 79*90 + 49; hence not 79 divides 7159 by NAT_4:9;
    7159 = 83*86 + 21; hence not 83 divides 7159 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7159 & n is prime
  holds not n divides 7159 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
