Problem 1065

../

---

Statement. Are there infinitely many primes $p$ such that $p=2^kq+1$ for some prime $q$ and $k\geq 0$? Or $p=2^k3^lq+1$?

Status. Open.

Source. erdosproblems.com/1065, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #1065, https://www.erdosproblems.com/1065.

References.

• [Gu04] Guy, Richard K., Unsolved problems in number theory. 3rd ed., Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp. Section B46 "The largest prime factor of $n$", printed p. 154, which the site's remark names, states the question in terms of the largest prime factor $P(p-1)$ of $p-1$: are there infinitely many primes $p$ with $(p-1)/P(p-1)=2^k$, or $=2^k\cdot 3^l$? Library home: guy_2004_unsolved_problems_number_theory.

Formalization. Statement in formal-conjectures.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• guy_2004_unsolved_problems_number_theory