Primes Arithmetic Progression (PAP) and CPAP

[Cybertronic]

is known !!!
https://www.primegrid.com/stats_ap26.php

[Cybertronic]

It is 403185216600637 + 9523 * 23# * n, n=0..22 and was found first as a normal AP-23 in 2006 by Markus Frind.
Joris Perrenet proved this as a minimal on 02 June 2023 !

https://www.pzktupel.de/JensKruseAndersen/RHMINEND.php

[Andrew Usher]

I assume there is nothing better than exhaustive search to do this; the basic technique is fairly obvious if I don't have it wrong - it just takes (at least) linear time in the size of the number.

One does not say in English 'proved as a minimal'; normal would be 'proved minimal' or 'proved to be minimal', I suppose 'as minimal' or 'as the minimal' would be acceptable or at least better than the version with the indefinite article.

An observation I just made is that for all AP longer than 10 for minimal end (6 for minimal start) that record does not also have the minimal difference, and that probably continues forever. But for CPAP, it is likely the exact opposite - the smallest always has minimal difference!

[Dr Sardonicus]

Originally Posted by Andrew Usher

<snip>
One does not say in English 'proved as a minimal'; normal would be 'proved minimal' or 'proved to be minimal', I suppose 'as minimal' or 'as the minimal' would be acceptable or at least better than the version with the indefinite article.
<snip>

Apart from it being pointlessly rude to be snippy about English grammar with someone whose first language may not be English, especially when the meaning is clear, you are failing to consider the possibility that the usage is correct.

Here is one way that this could be possible: Considering the AP-k's for various k, minimal end primes of AP-k are known for k = 3 to k = 23. The end prime of each such AP-k may thus properly be referred to as "a minimal" in the sense of being one among many.

[Cybertronic]

@Andrew Usher
I replaced to "proved to be minimal" .... und wehe das stimmt nicht !

Thanks for the hint.

[rudy235]

Originally Posted by Dr Sardonicus

Apart from it being pointlessly rude to be snippy about English grammar with someone whose first language may not be English, especially when the meaning is clear, you are failing to consider the possibility that the usage is correct.

Here is one way that this could be possible: Considering the AP-k's for various k, minimal end primes of AP-k are known for k = 3 to k = 23. The end prime of each such AP-k may thus properly be referred to as "a minimal" in the sense of being one among many.

I, too, see no need for such a correction. Was there a valid reason? None whatsoever.

[Andrew Usher]

I know that English is not his first language, and that's why I think correcting him may be helpful and not just rude (Actually, I'd correct a native speaker, too, if one wrote those exact words, but that would not happen.). However, it's more interesting that I seem to have discovered a new rule (or tendency) of English grammar, on something I'd never thought about until his phrase struck my ear as absolutely impossible.

[Cybertronic]

Guys, but am rather pleased when suggestions for a better wording come.
BTW, "proved this as a minimal" was a online-translater suggestion.

In German, we have hundreds of ways to formulate an issue. The translators then have to make something out of it.