Problems & Puzzles: Problems Problem 13.- The Gap of the Beast "A few moments ago I was
wondering what would be the smallest two *** Solution 18691113008663 + 666 = 18691113009329 Author: Mr. Marek Wolf (this information was sent by Mr. Wolf to Jud McCranie who sent it to Patrick De Geest who finally sent it to me yesterday, November 2, 1998) Correction: Mr. Wolf himself has sent the following e-mail comments: " ...The gap 666 really appears for the first time after prime 18691113008663. It can be found in J. Young and A. Pottler, "First occurrence prime gaps", Math. Comp. 52 (1989), p. 221. I have send to Jud the whole table of first occurences which I have at present at my disposal and I asked for credits when somebody will use my large data. I enclose this huge table below. It mainly comes from my own search up to 2^44 and remaining entries I have compiled from different sources, I should mention mainly Thomas Nicely, see http://www.lynchburg.edu/public/academic/math/nicely/ ....it is not true, that I have calculated all gaps up to 916, I have stopped after 716 when I have learned that Nicely is doing it also and that he reached over 10^15... Please notice my approximate formula for p: the first occurence of a gap d after a prime p: p ~ sqrt(d)*exp(sqrt(d)). The paper can be found on my www page: http://www.ift.uni.wroc.pl/~mwolf " |
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