|
 |
Gilbreath's conjecture
From TheBestLinks.com
Gilbreath's conjecture is a number theory problem about prime numbers. Write down all the prime numbers, like so:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
and then write down the absolute difference of subsequent values in the above sequence, and then do the same with the the resulting sequence. What you get looks like:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
- 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, ...
- 1, 0, 2, 2, 2, 2, 2, 2, 4, ...
- 1, 2, 0, 0, 0, 0, 0, 2, ...
- 1, 2, 0, 0, 0, 0, 2, ...
- 1, 2, 0, 0, 0, 2, ...
- 1, 2, 0, 0, 2, ...
Equivalently, let <math>a_n<math> be a value of the original sequence, and <math>b_n<math> be a value of the new sequence; then
- <math>b_n = |a_n - a_{n+1}|<math>.
The Gilbreath conjecture says that the first value of this sequence always equals 1, except for the original sequence of primes. It has been verified for primes up to 1013. It is attributed to N. L. Gilbreath, in 1958.
Related links
Top visited 0 of 0 links
[no links posted yet]
>> place link >>
Discussion
Last posted 0 of 0 messages
[no messages posted yet]
>> post message >>
Watch
You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
|
|
|
