(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?
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.
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Posted by Charlie
on 2007-08-19 14:44:29 |
computer exploration -- no proof -- spoiler
