Composite factors are not eligible:

153616228560877782360733142221974579132477827835600631264993134521609

= 7160401272398244691 * 219902328863708115073 * 97559577016295905770143558963

The smallest of them should have been found by TF, easily: 62 bits. (Wagstaff numbers have factors of form 2kp+1, just like Mersenne's.)

Let's find some even larger factors...

Code:

P-1 found a factor in stage #1, B1=100000.
2^8232929+1 has a factor: 8203927240046868961280630569987984778892578839825012457683394506843242760078451651993971

[292 bits]