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): $105$