Timeline for Where does the "Hardy-Littlewood" conjecture that $\pi(x+y) \leq \pi(x) + \pi(y)$ originate?
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| S Aug 24, 2025 at 6:03 | history | suggested | mick | CC BY-SA 4.0 |
improved title ; it was wrong and not tex
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| Aug 23, 2025 at 23:25 | review | Suggested edits | |||
| S Aug 24, 2025 at 6:03 | |||||
| Jan 6, 2015 at 2:28 | comment | added | Gerry Myerson | The question has since come up on math.stackexchange, see math.stackexchange.com/questions/1072194/… | |
| Nov 8, 2010 at 6:45 | answer | added | Gerry Myerson | timeline score: 12 | |
| Jul 7, 2010 at 21:05 | comment | added | T.. | Richards' paper from 1973 does both. It shows that the k-tuples conjecture rules out $\pi(n)$ being the (lim sup) densest packing of primes in an interval of length $n$. However, it refers to both the lim sup statement, and the stronger, non-asymptotic $\pi(x+y)$ inequality, as "conjectures" due to Hardy and Littlewood, citing Partitio Numerorum III. There is evidence both for and against the idea that H + L offered the limsup statement as a conjecture in PN3, but the nonasymptotic inequality doesn't appear anywhere in that paper. | |
| Jul 7, 2010 at 1:30 | comment | added | Will Jagy | Found it, section A9 in Guy (second edition), page 24. He does not give any reference to H-L in that section, although in A1, page 5, he mentions your same part number 3, then part number 6 in section D4, page 151. This could go back a very long way, essentially folklore with decades of authors misquoting the paper and then saying they do not believe the conjecture. Do Hensley and Richards correctly report on the H-L paper? Your language suggests that they do. | |
| Jul 6, 2010 at 23:43 | history | edited | T.. | CC BY-SA 2.5 |
fix Tex
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| Jul 6, 2010 at 22:51 | history | edited | Yemon Choi |
added history tag
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| Jul 6, 2010 at 22:43 | history | asked | T.. | CC BY-SA 2.5 |