[seqfan] Re: Prime numbers that differ by 30 with no primes between p and p+30

Harvey P. Dale hpd at hpdale.org
Wed Jan 1 01:27:09 CET 2020

```Chris:

You are correct that 69623 is the smallest prime such that its immediate predecessor prime and its immediate successor prime are both separated from it by 30. Here are the next such primes up through the 100,000th prime: 110681, 134639, 228677, 237821, 250919, 303187, 318949, 396479, 421943, 498301, 507461, 535273, 554347, 629653, 642457, 642487, 668273, 692191, 716033, 729821, 780553, 782611, 790927, 801247, 825161, 829319, 847423, 892321, 902903, 940127, 942479, 963943, 995273, 1027097, 1058891, 1058921, 1063273, 1072763, 1080383, 1090303, 1118599, 1123777, 1176323, 1193399, 1213981, 1234657.

That sequence does not appear in the OEIS. Is it of sufficient interest?
Best,
Harvey

-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Chris Thompson
Sent: Sunday, December 29, 2019 12:43 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Prime numbers that differ by 30 with no primes between p and p+30

I was motivated by David Seal's posting to wonder what the situation was for a similar but much better known series, namely prime pairs.

A001359 is the lesser of each pair, primes p such that p+2 is also prime

A006512 is the greater of each pair, primes p such hat p-2 is also prime

A001097 is their union as a set, with 5 occurring once

A077800 is their union as a multiset, with 5 occurring twice

It is probably not desirable that every sequence involving pairs should have all four versions in OEIS, though!

The union version for (p,p+30) being consecutive primes would face the same problem as for 5 with the prime pairs: should the p such that

(p-30,p,p+30) are consecutive primes, occur once or twice? [The smallest such p is 69623, and there are undoubtedly infinitely many of them.]

--

Chris Thompson

Email: cet1 at cam.ac.uk<mailto:cet1 at cam.ac.uk>

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