20180809, 23:24  #1 
"Dylan"
Mar 2017
499 Posts 
Primes in e
Following the threads regarding primes in pi (http://www.mersenneforum.org/showthread.php?t=16978) and phi (http://www.mersenneforum.org/showthread.php?t=21942), 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 http://mathworld.wolfram.com/IntegerSequencePrimes.html although that status is from 2016). Is anyone interested in doing the second part? 
20180810, 00:59  #2 
"Mark"
Apr 2003
Between here and the
5850_{10} Posts 
Here is the OEIS sequence 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. 
20180810, 03:31  #3 
Aug 2006
2^{3}×733 Posts 
http://oeis.org/A064118 is the main sequence.

20180810, 06:07  #4 
Romulan Interpreter
Jun 2011
Thailand
5·11·157 Posts 
[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] Last fiddled with by LaurV on 20180810 at 06:10 
20180810, 15:10  #5 
Aug 2006
2^{3}×733 Posts 
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.

20180810, 15:28  #6  
"Mark"
Apr 2003
Between here and the
2×3^{2}×5^{2}×13 Posts 
Quote:


20180810, 15:37  #7  
"Dylan"
Mar 2017
499 Posts 
Quote:


20180810, 16:59  #8  
Aug 2006
5864_{10} Posts 
Quote:


20180823, 15:33  #9 
"Dylan"
Mar 2017
499 Posts 
I have tested to 100,000 digits and confirmed all primes/PRP's up to that point. No primes/PRP's were missed. Continuing.

20181011, 00:55  #10 
"Dylan"
Mar 2017
499 Posts 
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 http://www.primenumbers.net/prptop/prptop.php, primes in pi are denoted by PIPrime(n), where n is an integer. 
20181011, 01:29  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
21570_{8} Posts 
floor(e*10^N)

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