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 Dylan14 2018-08-09 23:24

Primes in e

1 Attachment(s)
Following the threads regarding primes in pi ([URL]http://www.mersenneforum.org/showthread.php?t=16978[/URL]) and phi ([URL]http://www.mersenneforum.org/showthread.php?t=21942[/URL]), I have decided to start a thread looking for primes in e. I have attached the first million digits of e to the end of this post.

Like for pi and phi, there are two parts to the search:
1) Take the decimal expansion of e and locate primes in it, starting with the 2.
2) For each positive integer n, locate in the decimal expansion of e the first occurrence of the digits of the integer n, and then find the first prime constructed from the subsequent digits of e.

I am in the process of sieving 1) for the first million decimal digits of the expansion and I intend on testing that form in the hopes of finding a new e prime and to verify that none have been missed up to the current search limit (which is 197760 according to [URL]http://mathworld.wolfram.com/IntegerSequencePrimes.html[/URL] although that status is from 2016). Is anyone interested in doing the second part?

 rogue 2018-08-10 00:59

Here is the [URL="http://oeis.org/A007512"]OEIS sequence[/URL] for primes starting with the first digit of e.

With a small modification to pixsieve to output primes that it finds, there are only 2 starting terms < 100 with no primes under 1000 digits. 33 has a prime of length 1507. 42 has one of length 1470.

 CRGreathouse 2018-08-10 03:31

[url]http://oeis.org/A064118[/url] is the main sequence.

 LaurV 2018-08-10 06:07

[mod hat on] We are tempted to remove the big text attach, but let's ask first... Maybe we are worrying in vain, but you are wasting forum space and more important, wasting your attachments quota too... At least, it could be zipped, being only numbers it has a very good compression ratio.

Usually, people who join such effort are very much able to generate it with pari (just a simple command), or other tools, in (milli)seconds, or get it from web.
[mod hat off]

 CRGreathouse 2018-08-10 15:10

[QUOTE=LaurV;493556]Usually, people who join such effort are very much able to generate it with pari (just a simple command), or other tools, in (milli)seconds, or get it from web.[/QUOTE]

I can't really imagine someone being able to productively contribute to such a search, and yet being unable to generate the digits of e. YMMV.

 rogue 2018-08-10 15:28

[QUOTE=CRGreathouse;493545][url]http://oeis.org/A064118[/url] is the main sequence.[/QUOTE]

I know, but I don't see any real value in a sequence of "decimal length of primes" although I could see one argue that the primes themselves aren't very important either. Nevertheless, computing the decimal length of a PRP/prime is a no-brainer and a lot of sequences like this seem to clutter OEIS.

 Dylan14 2018-08-10 15:37

[QUOTE=LaurV;493556]We are tempted to remove the big text attach, but let's ask first... Maybe we are worrying in vain, but you are wasting forum space and more important, wasting your attachments quota too... At least, it could be zipped, being only numbers it has a very good compression ratio.

Usually, people who join such effort are very much able to generate it with pari (just a simple command), or other tools, in (milli)seconds, or get it from web.
[/QUOTE]

The only reason why I put the digits of e is simply just for convience for those who want to partake in the search. Although it is quite easy to generate them (y-cruncher generates the first million digits in about 2 tenths of a second on my hardware) and to find them on the web (a quick google search for decimal digits of e gives two links on the top of the results, one with 10k digits and one with 2M digits). If it is that much of a bother, feel free to remove the attachment.

 CRGreathouse 2018-08-10 16:59

[QUOTE=rogue;493597]I know, but I don't see any real value in a sequence of "decimal length of primes" although I could see one argue that the primes themselves aren't very important either. Nevertheless, computing the decimal length of a PRP/prime is a no-brainer and a lot of sequences like this seem to clutter OEIS.[/QUOTE]

The primes can be better for findability, the lengths are better for communication. Personally I can't get excited about either, I don't like base sequences.

 Dylan14 2018-08-23 15:33

I have tested to 100,000 digits and confirmed all primes/PRP's up to that point. No primes/PRP's were missed. Continuing.

 Dylan14 2018-10-11 00:55

I have tested to 200,000 digits and confirmed all primes/PRP's up to the old search limit of 197760. No primes were missed. Above the search limit, I found no new primes. Continuing.

Question: Is there a standard notation for designating an e prime? I ask since on [URL]http://www.primenumbers.net/prptop/prptop.php[/URL], primes in pi are denoted by PIPrime(n), where n is an integer.

 Batalov 2018-10-11 01:29

[c]floor(e*10^N)[/c]

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