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User talk:Bill McEachen

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Broken sequence links

Simply use A012345 instead of [[A012345]] ([[A012345]] gives A012345, i.e. it looks in OEIS Wiki instead of the Main OEIS). — Daniel Forgues 05:33, 27 June 2012 (UTC)

External links

The article for the Goldbach conjecture links two Helfgott papers. I think if we ask Helfgott himself, he'd be quite happy to have just the links to his papers, and not a link to a Wikipedia page which could potentially be used to spread lies about him. See <>. Alonso del Arte 04:20, 17 May 2014 (UTC)


Looking through the article history, maybe you are asking the question ? If so, using this link 1, what is computes seems to match your estimates:

  • n=1000 gave 28 vs "expected" 25
  • n=990 gave 52 vs "expected" 52

So it seems the issue is comparing expected to A002375 /2n.

[I cannot recall where this thread stems from ..., though I have notes on the pantonov website, which is corrected to be [1]]

(3) in the Q

A137328 the conjecture ought to read "odd prime number"
A338869 Conjecture: frequency of each value 1,2,6,30,210,... will be on the order of the primorial values themselves. (new seq coming ...)

A068670 Subsequence of A005377 (based upon its 66 terms)?
A172338 a(n+1) ~ A004767(n)- floor((A004767(n)-1)/125.4)
A087897 formula A087897(n+1) = A000009(n+1) - A000009(n)
A118754 Distinct entries stem from primes formed from odd composite numbers+ A002110(n), n>0.
A038767 WolframAlpha input: Select[{#, primorial(#) + prime(#+1)^2} & /@ Range[90], PrimeQ[#2] &]
Cf A245694. Extensions a(15)-a(16) due to Jon E. Schoenfield at A245694
A309720 comment: Correspond to where P(i)-(P(i+2)-P(i+1)) repeated values are seen.
(Pari) genit(maxx)={a=List();prevQ=0;listput(a,2);listput(a,3);listput(a,5);for(ptr=4,maxx,listput(a,prime(ptr)); q= a[ptr-2]-(a[ptr]-a[ptr-1]);if(q==prevQ,print1(q,","));prevQ=q);}
A084968 Besides 7, subset of A063163?
A079149 (Pari) genit(maxx)={a=List();prevx=4;forcomposite(x=5,maxx,q=x+prevx;if(q!=x^2-prevx^2,prevx=x;next);if(isprime(q),listput(a,q));prevx=x);forprime(y=2,floor(maxx/2.),if(setsearch(a,y),next);print1( y,","));}
A132435 Heavy overlap with A078972 (45 of the 52 entries there overlap).
A101328 is this just 1 followed by A016969 ?
A000217 formula: recurrence: a(n)= a(n-3) - 3*(a(n-2)-a(n-1)) with a(0..2)={0,1,3}
A271116 The composites of this sequence are a subset of A328662. Approx 99% of the entries are prime through the first 26128 entries (only 131 composites) submitted, enveloped by later comment
A333996 The first differences generate A014684(n2) for n2>1 submitted (altered to formula)
A276391 Entries are the first differences of A000695.(formula: a(n+1)=a000695(n+1)-a000695(n). submitted
A113636 comment a(n)= A014684(n+1) +1 submitted
A081267 Entries are the first differences of A050509(n2), n2>0. (formula a(n+1)=A050509(n+1)-A050509(n) submitted
A076639 A328662 Subsequence of A271116 submitted
A058199 For the first 500 entries, only 3 entries of A002182 are missed.submitted
A093599 Subsequence of both A030059 and A225228.submitted
A254528 comment removed
A137330. Primes 2&5 will never be seen

Very Large Prime, non-special form

(I will fiddle with the table formatting later)...

I have been working this of late. It was triggered by a post I saw.

I saw the blurp about "average" prime gap being 2.3*#digits.

Recognizing one need evaluate no more than 40% of numbers in a range, this becomes 0.92*#digits. With this gap, one might encounter from a random start a prime at the midway point, or 0.46*#digits. In the 10K digit zone, this might be 4600 candidate evaluations.

One can do MUCH better than this recognizing the role of primorials(A002110). There are several approaches, I will speak of one here. There well may be much better approaches, but I don't know of them.

One can use as a starting candidate p(N)# + p(N+1)# +1. Of course p(N)# +1 itself could be prime, call that adjacent iteration=0. We ignore that case for the discussion, as well as starting from primorial=30 (N=3). Here is a short list of the results, where iter=1 means p(N)# +1+ p(N+1)#, nextprime(1+p(N)#) +1+ p(N+1)#) is iter=2, etc.

PN #iterations Prime
5 1 37 2*3+2*3*5 (+1)
7 1 241 2*3*5*7+2*3*5 (+1)
11 1 2521 etc
13 1 32341
17 1 540541
19 2 10210219
23 1 232792561
29 3 6692786147

We presume we are using PRP here, but any subsequent confirmation involving a primality certificate quickly requires SIGNIFICANT RAM. For a 10K digit PRP this is >32Gb RAM. This approximation stems from a recent email exchange with RBaillie based upon his work. My laptop has 16Gb RAM, which is one limitation on related efforts. There are cloud server options but those can quickly be costly.--Bill McEachen (talk) 10:47, 2 February 2021 (EST)