
theorem Th37:
  641 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
A2: 2|^(4+2) = 16 * 4 by A1,NEWTON:8;
A3: 2|^(6+1) = 2|^6 * 2|^1 by NEWTON:8 .= 64 * 2 by A2;
A4:  5 = 2 * 2 + 1;
    641 = 5 * 2|^7 + 1 by A3;
    hence thesis by A3,A4;
  end;
