Primes of the form 2^p-p
- Thankyou to those observent people who spotted my typing error!
I meant to say that 2^p-p (for p being prime) doesn't yield any primes for p<20000 except for p<20 (not p=2 as in my previous mail).
Jens Kruse Andersen has checked upto p=60000 and still hasn't found any more primes.
Perhaps it might be worth looking into these a bit more?!?
It is unlikely though any PRPs found will be able to be proven prime since both +1/-1 tests aren't likely to have many factors....
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- If you allow not only primes but all odd numbers then
besides 3, 13 and 19, 2^p-p (p<10,000) is also
prime for p=9 and 21 and 3-PRP for
p=55, 261, 3415, 4185, and 7353.
Furthermore, the "PRP-Records" site lists 4 more PRP's:
2^108049-108049, 32526 digits
all found by Henri Lifchitz in 2001.