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

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## Source Work

1986: David Wells: *Curious and Interesting Numbers*:

- The Dictionary
- $105$

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

- The Dictionary
- $105$

## Mistake

*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 $75$.*

## Correction

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 $4$.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $105$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $105$