Previous such prime

Number Theory Level 4

$2017=2^{11}-2^5+1$

Given the equality above, what is the largest prime number $p\, (<2017)$ that could be represented as

$p=2^a \pm 2^b \pm 1?$

The answer is 1279.

1 solution

Maria Kozlowska
Jan 7, 2017

$2^{10}+2^8-1=\boxed{1279}$

Numbers that can be written as $2^a \pm 2^b \pm 1$ are called Solinas primes .

I'm enjoying how many ways you are coming up with to show that $2017$ is a "special" number. One suggestion: as the phrasing "What is a previous prime ..." is ambiguous since there are in fact $53$ primes that fit this description, it might be best to ask "What is the immediately previous prime ..." or "What is the next greatest prime ..." so that $1279$ is the unique answer.

Brian Charlesworth - 4 years, 5 months ago

I changed the wording.

Maria Kozlowska - 4 years, 5 months ago

Previous such prime

The answer is 1279.

1 solution

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