
theorem
  13313 is Proth
  proof
A1: 2|^2 = 2|^(1+1) .= 2|^1 * 2 by NEWTON:6 .= 2 * 2; then
    2|^(2+2) = 4 * 4 by NEWTON:8; then
    2|^(4+4) = 16 * 16 by NEWTON:8; then
A2: 2|^(8+2) = 256 * 4 by A1,NEWTON:8;
A3:  13 = 2 * 6 + 1;
    13313 = 13 * 2|^10 + 1 by A2;
    hence thesis by A2,A3;
  end;
