
theorem
  11777 is Proth
  proof
A1: 2|^2 = 2|^(1+1) .= 2|^1 * 2 by NEWTON:6 .= 2 * 2;
A2: 2|^(2+2) = 4 * 4 by A1,NEWTON:8;
A3: 2|^(4+4) = 16 * 16 by A2,NEWTON:8;
A4: 2|^(8+1) = 2|^8 * 2|^1 by NEWTON:8 .= 256 * 2 by A3;
A5:  23 = 2 * 11 + 1;
    11777 = 23 * 2|^9 + 1 by A4;
    hence thesis by A4,A5;
  end;
