Where is a list of Lehmer Pairs of zeros of zeta(s) ?

[Swamp Thing]

TL;DR

Where can we find a list of known Lehmer pairs of zeros of Riemann zeta?

Many sources (e.g. Wolfram Mathworld ) give the example of the 6709th and 6710th zeros of $\zeta$ i.e. where the imaginary parts of the argument are 7005.06266... and 7005.10056... respectively.

Where can we find a list of all known pairs? I tried searching "6709, 6710" on OEIS but that didn't help.

 

[jedishrfu]

The wiki article implies that these were the first and maybe only ones discovered so far. It seems the list is less interesting than some of the conjectures about them.

https://en.wikipedia.org/wiki/Lehmer_pair

in contrast, there are many zeros of the Riemann Zeta function.

http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html

and this paper by Varga

http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1145-3.pdf

 

[Swamp Thing]

Thank you.

Your post gave me an idea which somehow hadn't come to me before. I took the list of zeros from your link (Odlyzko, UMich) and pasted them into a spreadsheet. Then I took successive differences, and sorted them in ascending order of those differences. This gave me about 12 pairs that differ by less than the canonical example of root numbers 6709 and 6710. (I believe there is a formal definition that says how close is close enough to count as a Lehmer pair).