List Proth primes - MATLAB Cody - MATLAB Central

Problem 51758. List Proth primes

Created by ChrisR
Appears in Prime Numbers II

Difficulty:Rate

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As of datenum 738289, three of the twenty largest known prime numbers are Proth primes, prime numbers of the form  with . For example, taking  and  gives 3, the first Proth prime, and taking  and  gives 97, the sixth Proth prime. The number 199 is prime but not a Proth prime because . The number 49 is a Proth number (, ) but not prime.
Write a function to list the Proth primes between two limits a and b. Also provide the values of k and m. 
Optional: Values of k for which no values of  are prime are called Sierpinski numbers. Show that 78,557 is the smallest Sierpinski number. For more, see this page. 

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20 Solutions
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Last Solution submitted on Sep 11, 2024

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3 Comments

3 Comments

Dyuman Joshi on 2 Jun 2022

Chris, what if there are multiple pairs of (k,m) that result in a particular proth number, which pair should we report?

For example -

k=4, m=2, p=17
k=2, m=3, p=17
k=1, m=4, p=17

also
k=1, m=2, p=5
k=2, m=1, p=5

ChrisR on 7 Jun 2022

Good question, Dyuman. Please use the largest m possible.

Dyuman Joshi on 17 Jun 2022

Thanks for the clarification, Chris.
Nice question!

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