Integers such that Difference with Power of 2 is always Prime/Mistake

From ProofWiki
Jump to navigation Jump to search

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary


Erdős conjectured that [105] is the largest number $n$ such that the positive values of $n - 2^k$ are all prime. The only other known numbers with this property are $7$, $15$, $21$, $45$ and $75$.


First it should be noted that it should be specified that $k \ge 1$. Otherwise the statement is false: for example $7 - 2^0 = 6$ is composite.

Secondly, the list should also include $4$.