Talk:Proth prime

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Inconsistency

@數神: The lead:

A Proth number is a number N of the form

N=k2^{n}+1

where e and t are positive integers and

2^{n}>k

.

is inconsistent with the definition section:

A Proth number takes the form

N=k2^{n}+1

where

2^{n}>k,\ k,n\in \mathbb {N}

and

k

is odd.

in several ways, including:

in the lead formula, there is no e nor t corresponding to where e and t are positive integers;
in the lead, there is no requirement for k to be odd (as there is in the definition section);
in the definition section, it's unclear what the second k in $2^{n}>k,\ k,n\in \mathbb {N}$ means (perhaps $2^{n}>k,\ k\in \mathbb {N} ,n\in \mathbb {N}$ );
and assuming the lead means to say that n and k (not e and t) are positive integers, this seems different from the definition section requiring n being in the set $\mathbb {N}$ as ambiguously defined at at List of mathematical symbols#Symbols based on Latin letters, where it says $\mathbb {N}$ means either { 0, 1, 2, 3, ...} or { 1, 2, 3, ...}.

—[AlanM1(talk)]— 08:13, 11 December 2019 (UTC)[reply]

FWIW, the definition in the Sze paper (the first cite), says

N=2^{e}\cdot t+1

for some odd t with

2^{e}>t>0

. (1.1) —[AlanM1(talk)]— 08:25, 11 December 2019 (UTC)[reply]

So, I would suggest that both should say:

... number N of the form

N=k2^{n}+1

where k and n are positive integers, k is odd, and

2^{n}>k

.

—[AlanM1(talk)]— 09:08, 11 December 2019 (UTC)[reply]

Of course you are right about consistency, but in fact the requirement that k be odd is irrelevant: the set being defined does not change if we drop that condition. --JBL (talk) 15:26, 11 December 2019 (UTC)[reply]

den Boer reduction

Regarding the redlinked den Boer reduction, would it be useful to additionally cite or EL either:

Galbraith, Steven D. Mathematics of public key cryptography – Chapter 21 (PDF) (2.0 ed.). pp. 455–457 (PDF pp. 9–11). Retrieved 12 December 2019.

or maybe the older published version:

Galbraith, Steven D. (2012). "21.4.2". Mathematics of public key cryptography (PDF). Cambridge University Press. pp. 427–429. ISBN 9781107013926. Retrieved 12 December 2019.

(I haven't reviewed the differences) ? —[AlanM1(talk)]— 17:59, 12 December 2019 (UTC)[reply]