User talk:Bill McEachen

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 <http://wikipediocracy.com/2013/05/17/anonymous-revenge-editing-on-wikipedia-the-case-of-robert-clark-young-aka-qworty/>. Alonso del Arte 04:20, 17 May 2014 (UTC)

pending

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 ...)

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

etc

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)

A334472

I reported a WolframAlpha discrepancy Dec 31 2020 for Input: (2*gamma+log(8))/Pi. It is still broken as of 11/21/2021.--Bill McEachen (talk) 11:07, 21 November 2021 (EST)

A357776 script

genit(nterm=20)={arr=List();pr=List();dbg=0;eval1=0;eval2=0;odd=List();even=List();if(nterm%2!=0,nterm+=1);listput(odd,1);listput(even,2);listput(even,6);listput(odd,11); arr=List(setunion(Set(odd),Set(even)));print("initial seeds: ",arr[1]," ",arr[2]," ",arr[3]," ",arr[4]);while(#arr<nterm,mxev=0;mxod=0; for(ptr3=1,#arr,q=arr[ptr3];if(q%2==0&&q>mxev,mxev=q);if(q%2!=0&&q>mxod,mxod=q));prevCand2=mxod;fail2=1;while(fail2,cand2=0;eval2+=1;cand2=nextprime(prevCand2+1);prevCand2=cand2; if(eval2%100000==0,print("running (od) ...",eval2));if(cand2>0,fail2=0);for(ptr5=1,#arr,q=arr[ptr5];if(q%2==0&&!isprime(cand2+q),fail2=1;break))if(fail2>0,next); fail=1;ptrprev=0;dun=0;prevCand=mxev;while(fail>0,cand=0;eval1+=1;cand=prevCand+2;prevCand=cand;dun=1;if(eval1%100000==0,print("running (ev) ...",eval1," ",cand));if(dun>0,fail=0); for(ptr4=1,#arr,q=arr[ptr4];if(q%2!=0&&!isprime(cand+q),fail=1;break));if(!isprime(cand2+cand),fail=1);if(fail>0,next));listput(even,cand);listput(odd,cand2); arr=List(setunion(Set(odd),Set(even))));arr=List(setunion(Set(odd),Set(even))));for(i=1,#odd,for(j=1,#even,w=odd[i];z=even[j];listput(pr,w+z)));listsort(pr);arr;}