Talk:Higgs prime

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Definition[edit]

The current definition seems inconsistent about whether Higgs primes are only defined for squares. I think the algebraic form is unnecessarily complicated and unclear. The name Hp_n seems unfortunate because it can be read as H*p_n, and why say \phi(Hp_n) instead of just Hp_n-1. And \pi(Hp_n) > \pi(Hp_{n-1}) is apparently only used to indicate that Hp_n is the nth Higgs prime.

I don't know how the listed references formulate the definition, but I suggest this:

In number theory, for a given positive integer exponent a, a Higgs prime is a prime number p for which p − 1 divides the ath power of the product of the smaller Higgs primes (equivalently, all prime factors of p − 1 are Higgs primes, and no prime factor has multiplicity larger than a). Sometimes a = 2 is assumed. PrimeHunter 15:35, 23 February 2007 (UTC)

The needlessness of invoking the prime counting function was also mentioned at PlanetMath, and I simplified it there as now I do here. But this is Wikipedia and not PlanetMath, and if after reading the listed references you're confident that your rewording is better, go ahead and reword it. You don't have to get my permission. You might be able to access the Burris and Lee paper through jstor.org. PrimeFan 22:30, 23 February 2007 (UTC)

Prime-counting function is designated with \phi\!\, within TeX markup, not as usual \pi\!\,. I guess it is just a typo. --xJaM 16:39, 13 July 2007 (UTC)

No, not a typo, but unnecessary mention of π(x) which has not been used since this edit. I have removed π(x) and explained that Φ(x) is Euler's totient function: [1]. PrimeHunter 18:03, 13 July 2007 (UTC)