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.
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.
are prime are called Sierpinski numbers. Show that 78,557 is the smallest Sierpinski number. For more, see this page. Solution Stats
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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
Good question, Dyuman. Please use the largest m possible.
Thanks for the clarification, Chris.
Nice question!