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This is an extension of this question and this question on MathStackExchange.

I have developed a formula for almost primes which is far more accurate asymptotically than Landau's well known

$$\pi_k(n) \sim \left( \frac{n}{\log n} \right) \frac{(\log\log n)^{k-1}}{(k - 1)!}$$

and I have a paper that I would like to submit to arXiv.org, whilst it is in the process of being reviewed (which I realise can take a very long time).

However, the submission guidelines say that it must be endorsed by someone currently affiliated with ArXiv. I have heard that it is possible to publish on vixra.org, but that it is not really advisable.

I don't know whether this is an appropriate question to ask, but users on MathStackExchange have suggested that I ask here whether anyone would be willing to endorse a publication of the paper on ArXiv.

I am not affiliated with any university - I just have a (an over?!) healthy interest in the subject! Unfortunately, I do not know of anyone in the field, and am a little wary of sending the paper to people I do not know.

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    $\begingroup$ I don't think that it is appropriate to use MO to ask for arXiv endorsements, so I have voted to close. I saw on math.stackexchange.com that Igor Rivin told you he'd be willing to look at your paper. I urge you to take him up on his kind offer. I'm sure if he thinks it is correct and new that he will either be willing to endorse it himself or at least suggest other people who might be willing to. $\endgroup$ Jan 4, 2014 at 18:44
  • $\begingroup$ OK - many thanks for your suggestion. $\endgroup$
    – martin
    Jan 4, 2014 at 18:46
  • $\begingroup$ It will also be probably appropriate to ask here if your more exact formula is new, likely to be correct, etc. (while presenting it). I am not familiar with vixra.org but if you want your paper to be "recorded," and if there is no endorsement needed, I dont see why it is not advisable. $\endgroup$
    – Gil Kalai
    Jan 4, 2014 at 19:07
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    $\begingroup$ Oh, no, don't use vixra. Bad advice from Gil, since he is not aware of what appears there. $\endgroup$ Jan 4, 2014 at 19:14
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    $\begingroup$ @GilKalai : vixra is basically arxiv for crackpots. $\endgroup$ Jan 4, 2014 at 19:33

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I don't know anything about almost primes, but I think you're mistaken not to send your paper to people in the field. If you're afraid of someone stealing your idea, I wouldn't worry --- having already submitted it to a journal establishes your priority (besides the fact that having your idea stolen seems very unlikely in this situation). A much more likely outcome is that your paper won't be read. However, if you do the research to find people who would be interested in this exact problem --- which, if you have internet, should be easy --- you increase the chance of being read. Being polite and asking for suggestions could also be more likely to produce a helpful response.

Most professional mathematicians are not interested in stealing your ideas, but are very interested in encouraging others who share similar interests. Approach others with this in mind.

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    $\begingroup$ It's true that there are exceptions, but once you've put it out there the possibility of appropriation is virtually nil. Posting your formula here on MO, as Gil suggests, would also ensure priority. Good luck! $\endgroup$
    – Nik Weaver
    Jan 4, 2014 at 20:38
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    $\begingroup$ One more thing. Professional number theorists know an awful lot about primes. Be prepared for the possibility that your idea has already appeared somewhere. $\endgroup$
    – Nik Weaver
    Jan 4, 2014 at 20:41
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    $\begingroup$ @martin : please don't post it here. it is well-established that it is not appropriate to use mo to publicize your work. I think you are misunderstanding what Nik Weaver is saying. $\endgroup$ Jan 4, 2014 at 21:19
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    $\begingroup$ Incidentally, it was never my intention to use MO as a platform to publicize my work! $\endgroup$
    – martin
    Jan 4, 2014 at 23:09
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    $\begingroup$ @martin : don't worry, I know that you have not tried to do so. I just wanted to prevent an unpleasant situation from developing. Good luck with your research! $\endgroup$ Jan 5, 2014 at 1:21

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