Talk:Prime power

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I would like to find a Prime number >10 power 15, could some one help me out. Thanks

2^30,402,457 − 1, see Mersenne prime for known large primes. Charles Matthews 19:36, 29 August 2006 (UTC)

prime powers in arithmetic sequences

Are there results on generalizations to Dirichlet's theorem on infinitely many primes in arithmetic sequences? Like, if (a,b)=1, might there be infinitely many squares of primes in the set {a + nb}?Rich 17:26, 19 September 2006 (UTC)

Definition

@JayBeeEll: Hi, I changed the definition because in a true definition subject and object should be in its correct position. In

In mathematics, a prime power is a positive integer power of a single prime number.

The subject is "power", but it is not correct, subject should be a prime number, I persist that this definition is more illustrative:

In mathematics, a prime power is a prime number to the power of a positive integer.

Additionally, the word "single" in the first definition is redundant, we have "prime number" and "composite number", here "single" is redundant. Hooman Mallahzadeh (talk) 17:09, 17 December 2021 (UTC)

While I agree that the sentence is, at present, somewhat awkward, your revised version is much more awkward. The theory you put forward here (ignoring the misuse of the word "subject") is definitely wrong: the word "power" can refer both to the exponent and to the result of exponentiation ("8 is a power of 2" is idiomatic mathematical English, at least where I'm from) so a prime power is a power, but a prime power is most certainly not a prime number. If I get some time (& remember) I will think about how else that sentence could be made clearer. --JBL (talk) 22:07, 18 December 2021 (UTC)|

I agree with JBL. Moreover your formulation would make incorrect sentences such as "8 and 9 are prime powers", which are not only correct, but also commonly used in mathematics (see the second paragraph of Finite field for an example in Wikipedia). D.Lazard (talk) 09:23, 19 December 2021 (UTC)