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A129870
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Difference between the (10^n)-th and the (10^n-1)-th prime.
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0
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6, 18, 12, 6, 20, 6, 2, 4, 12, 12, 20, 12, 22, 26, 30, 6, 72, 152, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is interesting that the number 2 occurs deep into the sequence indicating a twin prime pair. It is reasonable to ask if this will ever occur again. Similarly, the analogous sequence A074383, "Difference between (1+10^n)-th and (10^n)-th primes" has 2 occurring shallow into the sequence. It is reasonable to ask if the number 2 will ever occur again in that sequence. The link provides an excellent algorithm, primex(n), that I developed to find the n-th prime using Gram's approximation of Riemann's approximation R(x) for Pi(x). Primex(n) will give about n/2 exact digits for prime(n). For A006988 (18), primex(18) is 44211790234127235469.62904554...This is only as good as R (x) but nevertheless is superior to the exact formulas out there from a practical stand point. If we apply the code gpx(n) = for(x=1,n,y=nextprime(primex(10^x))-nextprime (primex(10^x-1));print1(floor(y)",")), we will get the eratic concoction 2,0,8,14,22,28,26,0,72,18,22,0,0,0,0,0,32,0,80,78,60,0 as an analytical counterpart of the sequence given.
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LINKS
| C. Hilliard, Nth prime approx.
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EXAMPLE
| The (10^18)-th prime or A006988(18) = 44211790234832169331.
Using PARI, precprime(A006988(18)-1) = 44211790234832169179.
The difference is 152, the last entry in the table.
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CROSSREFS
| Cf. A006988, A074383.
Sequence in context: A074923 A093061 A078741 * A091014 A097370 A174904
Adjacent sequences: A129867 A129868 A129869 * A129871 A129872 A129873
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Jun 04 2007
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EXTENSIONS
| a(19) from Max Alekseyev (maxale(AT)gmail.com), May 13 2009
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