# Prime Search 3^n – n + 1

I’ve started sieving the prime numbers of the form:

I’ve also submitted the sequence to OEIS (it’s still a draft with the number A308829). The last value I’ve found is:

The numbers are very small if compared to the last Mersenne or GFN primes found, but I’m confident to overcome a million digits very soon. The sieving process is quite slow but it can be limited to odd values of n because, if n is even:

The sieving program I’ve written is obviously in C++ and it’s currently based on GMP and Intel TBB®, but I’m working to improve the performances every day. The following ones are snippets in common mathematical languages to find the first terms of the sequence:

#### Mathematica® snippet

a[k_] := Block[{seq = {}, n = 0, i = 0}, While[Length[seq] < k, {n = 3^i - i + 1, If[PrimeQ[n], AppendTo[seq, i]], i += 1}]; seq]

#### Sage snippet

def list_a(k):

return [i for i in range(k) if (3**i) - i + 1 in Primes()]

#### PARI snippet

a(k) = isprime(3^k - k + 1); \\ Jinyuan Wang, Aug 03 2019

### Length of the primes

### Full list of found primes

### Help needed!

If you want to help me in the research of the primes, please send me a private message. You can also make a donation through Paypal to support all the monthly expenses for the servers.