Problem 1688. Prime Sequences: AP-k Minimum Final Value
Welcome to Fun with Primes. Today we will find the Minimum Final Value AP-k sequences for n_max=3:12 given the primorial and knowledge that the solution is of the form a + b * k# * n.
The AP-k of n sequence is n_max+1 primes of the form a + b * k# * n where n=0:n_max. The value of "a" is a prime and k# is the primorial.
The primorial k# is the product of all primes ≤ k, e.g. 10# = 2 · 3 · 5 · 7.
Input: (k, n_max)
Output: [a, b] for the equation Prime = a + b * k# * n, n=0:n_max; Prime(n_max) must be the optimum minimum.
Value Range Limits: [a<150,000 , b<8 ]
Example:
(13, 13) yields [31385539,14 ]; 31385539 + 14·13#·n (End Prime 36850999)
Commentary:
(13, 16) has a non-minimal end [17, 11387819007325752 ] to give Primes=17 + 11387819007325752·13#·n
The current June 2013 record for n is 25 via PrimeGrid: 43142746595714191 + 23681770·23#·n
Solution Stats
Problem Comments
-
1 Comment
Did Cody decrease the maximum time you can run a solution before it times out? My previous solutions were about 16-18 sec on my box, but timed out here. The one that finally worked was at around 13 sec on my box.
Solution Comments
Show commentsProblem Recent Solvers4
Suggested Problems
-
72 Solvers
-
577 Solvers
-
Side of an equilateral triangle
5777 Solvers
-
315 Solvers
-
There are 10 types of people in the world
1002 Solvers
More from this Author294
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!