

A172483


Are consecutive cousin primes infinite?


1



1, 1, 2, 5, 4, 4, 2, 6, 4, 7, 7, 5, 9, 12, 13, 14, 14, 9, 12, 10, 11, 13, 20, 16, 15, 16, 15, 23, 19, 22, 26, 27, 28, 26, 22, 20, 27, 25, 27, 28, 26, 35, 29, 29, 29, 30, 45, 30, 36, 22, 30, 39, 39, 40, 44, 44, 43, 34, 38, 36, 48, 54, 43, 38, 43, 49, 45, 47, 53, 38, 51, 51, 62, 56
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OFFSET

1,3


COMMENTS

If you graph the order of the consecutive cousin primes along the xaxis (i.e., first pair of cousin primes, second, third,...) and the number of cousin primes in the sequence given above along the yaxis, a clear pattern emerges. As you go farther along the xaxis, greater are the number of consecutive cousin primes, on average, within the interval obtained. If one can prove that there's at least one consecutive cousin prime within each interval, this would imply that cousin primes are infinite. I suspect the number of consecutive primes within each interval will never be zero. Can you prove it?


REFERENCES

C. C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Perseus Books, 1999.
M. D. Sautoy, The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, HarperCollins Publishers Inc., 2004.


LINKS

J. S. Cheema, Table of n, a(n) for n = 1..1103


EXAMPLE

Take any pair of consecutive cousin primes. Let us say the very first one (7,11). Square the first term, you get 49, then take the product of the two primes, you get 7x11=77. Between these two numbers, namely (49,77) there is 1 consecutive cousin prime (67,71). Hence the very first term of the sequence is 1, and so on.


PROG

(Other) A SAS program written by Rick Aster was used as my starting point. The program can be found at this link: www.globalstatements.com/shortcuts/88a.html


CROSSREFS

Cf. A023200, A046132, A087679.
Sequence in context: A266401 A083798 A197377 * A211247 A021397 A325941
Adjacent sequences: A172480 A172481 A172482 * A172484 A172485 A172486


KEYWORD

nonn


AUTHOR

Jaspal Singh Cheema, Feb 04 2010, Feb 17 2010


STATUS

approved



