# Talk:Cuban prime

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Field: Number theory

## Name

This article could use some clarification... the name doesn't come from cubes, and doesn't come from Cuba, then what does it come from? 8.8.202.167 01:24, 29 June 2007 (UTC)

It comes from cubes as the article says. I have added a reference to http://mathworld.wolfram.com/CubanPrime.html which also says it. However, deriving "cuban" from "cube" doesn't sound normal to me. Maybe the person who named them deliberately made a derivation of "cube" that would become another word, but that's just speculation on my part. PrimeHunter 02:44, 29 June 2007 (UTC)
The most obvious alternative would be "cubic prime," but that makes me think of a number that is both prime and a perfect cube. Even if you accept 1 as a prime number, there would only be one such number. PrimeFan 21:36, 29 June 2007 (UTC)
Google found that "cubic prime" [1] is used for the cube of a prime in [2], but maybe the term was invented for the puzzle. PrimeHunter 22:52, 29 June 2007 (UTC)
Interesting. I too am inclined to think that it was invented for the puzzle. PrimeFan 20:44, 30 June 2007 (UTC)

## Why x = y + 1 ?

I don't see the point of the additional restriction "x=y+1 or x=y+2". These should be lifted off the definition. MathWorld doesn't have them, for instance. In later sections one can then study (or rather just mention) the subsets obtained by fixing x-y. --FvdP (talk) 19:06, 11 January 2010 (UTC)

Actually, the referenced MathWorld article only handles the x=y+1 case. Yet I'm still wondering, why stop at these 2 cases ? Because they're the only ones who have received significant attention ? --FvdP (talk) 19:12, 11 January 2010 (UTC)

## Validating the largest known Cuban prime

The article says "As of January 2006 the largest known has 65537 digits with [number], found by Jens Kruse Andersen.". How do we validate that? I can navigate to the page to see the number, but what tells us there is no larger one? Can someone explain how to use the site to find the current largest Cuban prime? Coastside (talk) 12:33, 2 June 2012 (UTC)

I'm Jens Kruse Andersen. I added the claim in January 2006 [3] as my third edit, before learning more about Wikipedia. At the time it was in the 5000 largest known primes at [4], but it was still non-trivial to see whether it was the largest listed Cuban prime. The 5000 largest primes at the time can be found via the Prime Pages search page [5] by selecting Age, "all verified primes" and 5000, but that's also non-trivial. Assuming the database is complete (not quite but it's close) it contains all primes which were among the 5000 largest at the time of discovery, but that's insufficient to determine whether it's the largest known Cuban prime today. Many primes found since 2006 are larger than 65537 digits but were not in the top-5000 at the time. Cuban primes attract very little attention. In fact I have never heard of anybody other than myself who searched large examples, and I only did it once. It's unlikely anybody will find a large prime which is a Cuban prime unless they specifically searched for Cuban primes. It's probably still the largest known but there is no source. Fortunately there is a source saying it was the largest known as of January 2006: http://primes.utm.edu/curios/page.php?number_id=5988. I submitted it but Prime Curios at the Prime Pages has editors who review submissions and I'm not among them. They know me over the Internet as a serious prime searcher and I assume they didn't actually attempt to test my submission. I have a conflict of interest but I suggest adding http://primes.utm.edu/curios/page.php?number_id=5988 as an additional or replacement source, and keep the "As of January 2006" statement with no year update. PrimeHunter (talk) 15:58, 2 June 2012 (UTC)

## Two names needed

As the two types seem to be largely or entirely distinct, they need two different names. — Preceding unsigned comment added by 86.181.10.231 (talk) 12:34, 20 December 2013 (UTC)

As the cubes cancel down to squares, even the word "Cuban" is rather silly. — Preceding unsigned comment added by 86.181.10.231 (talk) 12:24, 27 December 2013 (UTC)
Maybe so, but Wikipedia is based on verifiable reliable sources. The sources about Cuban primes do use that name. PrimeHunter (talk) 19:48, 27 December 2013 (UTC)