Editing Formula for primes (section)

==Possible formula using a recurrence relation==
Another prime generator is defined by the [[recurrence relation]]
:<math> a_n = a_{n-1} + \gcd(n,a_{n-1}), \quad a_1 = 7, </math>
where gcd(''x'', ''y'') denotes the [[greatest common divisor]] of ''x'' and ''y''. The sequence of differences ''a''<sub>''n''+1</sub> − ''a<sub>n</sub>'' starts with 1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 3, 1, 5, 3, ... {{OEIS|id=A132199}}. {{harvtxt|Rowland|2008}} proved that this sequence contains only ones and prime numbers. However, it does not contain all the prime numbers, since the terms gcd(''n'' +&thinsp;1, ''a<sub>n</sub>'') are always [[parity (mathematics)|odd]] and so never equal to 2. The same paper conjectures that the sequence contains all odd primes: in fact, 587 is the smallest odd prime not appearing in the first 10,000 outcomes different from 1.<ref>{{Citation |last1=Rowland |first1=Eric S. |title=A Natural Prime-Generating Recurrence |journal=Journal of Integer Sequences |volume=11 |issue=2 |pages=08.2.8 |year=2008 |url=http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html |arxiv=0710.3217 |bibcode=2008JIntS..11...28R}}.</ref>

This recurrence is rather inefficient. In perspective, it is trivial to write an algorithm to generate all prime numbers (from the definition), and many [[Generating primes|more efficient algorithms]] are known. Thus, such recurrence relations are more a matter of curiosity than of practical use.