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  1. Path: sparky!uunet!sun-barr!cs.utexas.edu!uwm.edu!ogicse!das-news.harvard.edu!husc-news.harvard.edu!ramanujan!elkies
  2. From: elkies@ramanujan.harvard.edu (Noam Elkies)
  3. Newsgroups: sci.math
  4. Subject: Re: 2n = difference of primes?
  5. Message-ID: <1992Sep4.233520.15379@husc3.harvard.edu>
  6. Date: 5 Sep 92 03:35:19 GMT
  7. Article-I.D.: husc3.1992Sep4.233520.15379
  8. References: <92248.16510732WENPW@CMUVM.CSV.CMICH.EDU>
  9. Organization: Harvard Math Department
  10. Lines: 12
  11. Nntp-Posting-Host: ramanujan.harvard.edu
  12.  
  13. In article <92248.16510732WENPW@CMUVM.CSV.CMICH.EDU>
  14. 32WENPW@CMUVM.CSV.CMICH.EDU writes:
  15. >Question:  Is it true that every [even] positive integer 2n is the
  16. >difference of some pair of primes?
  17. >(2 = 5-3, 4 = 7-3, 6 = 11-5, 8 = 13-5, 10 = 13-3, ...?)
  18.  
  19. Yes.  Or rather, it is next-to-certainly true.  But nobody at present
  20. knows how to prove it for even one value of n.  For instance (n=1) the
  21. twin-prime conjecture is still open.
  22.  
  23. --Noam D. Elkies (elkies@zariski.harvard.edu)
  24.   Dept. of Mathematics, Harvard University
  25.