TOPICS
Search

Primitive Prime Factor


Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It is possible for a term a_n to have zero, one, or many primitive prime factors.

For example, the prime factors of the sequence {k^2+1}_(k=1)^(10) are summarized in the following table (OEIS A005529).

kk^2+1prime factorizationprime factorsprimitive prime factors
12222
25555
3102·52, 5emptyset
417171717
5262·132, 1313
637373737
7502·5^22, 5emptyset
8655·135, 13emptyset
9822·412, 4141
10101101101101

See also

Prime Factor, Prime Factorization, Primitive Root

Explore with Wolfram|Alpha

References

Sloane, N. J. A. Sequence A005529/M1505 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Primitive Prime Factor

Cite this as:

Weisstein, Eric W. "Primitive Prime Factor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimitivePrimeFactor.html

Subject classifications