All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Getting Primes With 2 And 4 (Posted on 2007-08-19)
(A) Determine all possible prime numbers f such that each of (f+1)/2 and (f-1)/4 are prime numbers.

(B) What are the possible prime numbers g such that each of (g+1)/4 and (g-1)/2 are prime numbers?

 See The Solution Submitted by K Sengupta Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer exploration -- no proof -- spoiler | Comment 1 of 6

In testing the primes under 100,000,000, only 13 met the first set of criteria, and only 9 and 11 met the second set of criteria.

`   10   P=2   15    loop   20     T1=(P+1)//2:T2=(P-1)//4   30     if T1=int(T1) and T2=int(T2) then if prmdiv(T1)=T1 and prmdiv(T2)=T2 then print P,T1,T2   40     T1=(P+1)//4:T2=(P-1)//2   50     if T1=int(T1) and T2=int(T2) then if prmdiv(T1)=T1 and prmdiv(T2)=T2 then print tab(40);P,T1,T2   55     P=nxtprm(P)   56     if P>100000000 then goto 100   60    endloop  100   end`

The results were:

`                                         3       1       1 5       3       1                                         7       2       3                                         11      3       5 13      7       3`

where the left column reported potential solutions to the first set, and the right column to the second set.  But the first found potential solutions included derived "primes" that were one or both equal to 1, which is non-prime.

 Posted by Charlie on 2007-08-19 14:44:29
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information