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

[Harvey P. Dale]

Edwin:

            Yes, thanks. There are 34 such quadruples up through the 1 millionth prime.
           Best,
           Harvey



-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of W. Edwin Clark
Sent: Tuesday, December 31, 2019 8:18 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



And... based on your data: Here are the only two quadruples of successive primes of the form [p,p+30,p+60,p+90] up through the 100,000th prime:

  [642427, 642457, 642487, 642517]

  [1058861, 1058891, 1058921, 1058951]



On Tue, Dec 31, 2019 at 7:27 PM Harvey P. Dale <hpd at hpdale.org<mailto:hpd at hpdale.org>> wrote:



> 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<mailto: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<mailto: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<mailto:cet1 at cam.ac.uk%3cmailto:cet1 at cam.ac.uk>>

>

>

>

>

>

>

>

>

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