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Difference between revisions of "Gilbreath conjecture"

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<TR><TD valign="top">[1]</TD> <TD valign="top">  Andrew M. Odlyzko, "Iterated absolute values of differences of consecutive primes", ''Math. Comput.'' '''61''', no.203  (1993) pp.373-380 {{DOI|10.2307/2152962}} {{ZBL|0781.11037}}</TD></TR>
 
<TR><TD valign="top">[1]</TD> <TD valign="top">  Andrew M. Odlyzko, "Iterated absolute values of differences of consecutive primes", ''Math. Comput.'' '''61''', no.203  (1993) pp.373-380 {{DOI|10.2307/2152962}} {{ZBL|0781.11037}}</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  Richard K. Guy, "Unsolved problems in number theory" (3rd ed.) Springer-Verlag (2004) ISBN 0-387-20860-7 {{ZBL|1058.11001}}</TD></TR>
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<TR><TD valign="top">[2]</TD> <TD valign="top">  Richard K. Guy, "Unsolved problems in number theory" (3rd ed.) Springer-Verlag (2004) {{ISBN|0-387-20860-7}} {{ZBL|1058.11001}}</TD></TR>
 
<TR><TD valign="top">[3]</TD> <TD valign="top">  Norman Gilbreath, "Processing process: the Gilbreath conjecture", ''J. Number Theory'' '''131''' (2011) pp.2436-2441 {{DOI|10.1016/j.jnt.2011.06.008}} {{ZBL|1254.11006}}</TD></TR>
 
<TR><TD valign="top">[3]</TD> <TD valign="top">  Norman Gilbreath, "Processing process: the Gilbreath conjecture", ''J. Number Theory'' '''131''' (2011) pp.2436-2441 {{DOI|10.1016/j.jnt.2011.06.008}} {{ZBL|1254.11006}}</TD></TR>
 
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Latest revision as of 19:26, 14 November 2023

2020 Mathematics Subject Classification: Primary: 11A41 [MSN][ZBL]

A conjecture on the distribution of prime numbers.

For any sequence $(x_n)$, define the absolute difference sequence $\delta^1_n = |x_{n+1} - x_n|$, and the iterated differences $\delta^{k+1} = \delta^1 \delta^k$. In 1958 N. L. Gilbreath conjectured that when applied to the sequence of prime numbers, the first term in each iterated sequence $\delta^k$ is always $1$. Odlyzko has verified the conjecture for the primes $\le 10^{13}$.

References

[1] Andrew M. Odlyzko, "Iterated absolute values of differences of consecutive primes", Math. Comput. 61, no.203 (1993) pp.373-380 DOI 10.2307/2152962 Zbl 0781.11037
[2] Richard K. Guy, "Unsolved problems in number theory" (3rd ed.) Springer-Verlag (2004) ISBN 0-387-20860-7 Zbl 1058.11001
[3] Norman Gilbreath, "Processing process: the Gilbreath conjecture", J. Number Theory 131 (2011) pp.2436-2441 DOI 10.1016/j.jnt.2011.06.008 Zbl 1254.11006
How to Cite This Entry:
Gilbreath conjecture. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gilbreath_conjecture&oldid=54464