Prime number was a good articles nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Under "number of prime numbers below a given number" section, you might want to add the derivative of pi(n) n/ln(n) which is [ln(n)-1]/[[ln(n)]^2], which gives the approximate fraction of prime numbers at a certain 'size' number. For example, at the 1,000,000,000 level, you can expect about 46 out of 1000 numbers to be prime. 220.127.116.11 (talk) 19:37, 7 September 2014 (UTC)
This might be true, but it is something of a statement of the obvious. — Preceding unsigned comment added by 18.104.22.168 (talk) 13:49, 15 January 2015 (UTC)
It is also unnecessarily complicated, as the simpler 1/ln(n) is asymptotically the same, and it's only an asymptotic formula anyway. The editor who uses the pseudonym "JamesBWatson" (talk) 15:13, 24 February 2015 (UTC)
"There is no known useful formula that sets apart all of the prime numbers" - is there a useless one? What does "useful" mean? Are there formulas that require computing power beyond our abilities? --Richardson mcphillips (talk) 17:52, 6 February 2015 (UTC)
There are formulas that are not useful because they involve functions that are defined in terms of prime numbers, so using them to compute prime numbers would be circular reasoning. —David Eppstein (talk) 18:56, 6 February 2015 (UTC)
There are also formulas whose application requires so much computation that it would be faster to use trial division. For example, Wilson's theorem. —Mark Dominus (talk) 20:53, 6 February 2015 (UTC)
The lead is only supposed to summarize the article. Prime number#Formulas for primes goes into more detail. It's hard to give a short precise statement (or even a long one) about what is lacking to have a "good" formula but such a lack is often mentioned, and lots of people have searched and still search for it, whatever "it" is. I think it's appropriate to give some hint in the lead that we don't have the kind of formula we would like. PrimeHunter (talk) 01:47, 7 February 2015 (UTC)
New section: The Interval Containing At Least One Prime Number needed.
It seems like someone forgot to have a section on the Interval Containing At Least One Prime Number. So, I will suggest it. John W. Nicholson (talk) 17:55, 1 March 2015 (UTC)
As most people are not mind-readers, probably it would be a good idea to include in your suggestion enough information for other editors to have some clue what you are talking about. Something related to prime gaps? --JBL (talk) 18:01, 1 March 2015 (UTC)
An example from Dusart 2010, for x>= 396738, the interval [x, x + x/(25ln^2(x))] contains at least one prime. I know there is a history of other statements like this. John W. Nicholson (talk) 19:38, 18 March 2015 (UTC)
Article contradicts with other wikipedia article.
The article claims that the latest prime number was found in April 2014 and later in the sentence links to the wikipedia list of largest prime numbers. However, that article claims that the latest largest prime number was discovered in February 2013. 22.214.171.124 (talk) 16:13, 14 April 2015 (UTC)
The article currently says "As of April 2014, the largest known prime number has 17,425,170 decimal digits." Here "As of" isn't meant to be a discovery date but a date where the statement was known to be valid (it's also valid today). If it only said "The largest known prime number has 17,425,170 decimal digits", then it would become invalid when the record is broken. The record would probably quickly be updated in our own article but we also have many reusers who copy our articles without updating their copies. See more at Wikipedia:As of. PrimeHunter (talk) 16:31, 14 April 2015 (UTC)