Before trying the problems "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

Is 7013*2ⁿ+1 always composite?

Is 78557*2ⁿ+1 always composite?

(In reply to Does it continue? by Jer)

It's an interesting question, Jer.

For my part, I freely admit I had no instinctive opinion as to the pattern in these cases.

Having looked at the forthcoming problems in the queue, without attempting to solve:

3: No reason to think so.

4: Yes, almost certainly.

5,6: Reasonably obvious.

I look forward to proving myself wrong in due course.

Meanwhile, thank you for your kind words!

Edited on September 18, 2017, 3:53 am

Posted by broll on 2017-09-17 23:05:37