[seqfan] Re: Prime numbers that differ by 30 with no primes between p and p+30
W. Edwin Clark
wclark at mail.usf.edu
Wed Jan 1 02:17:43 CET 2020
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> 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> 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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