## Another Qaudratic form??

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• Guys, I ve been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting
Message 1 of 2 , Jan 10 12:00 PM
Guys,
I've been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting ones so far are:

1. 4^k +/- 61*2^(k-1) - 1

2. 4^k +/- 139*2^(k-1) - 1

If P is not prime, then R would not be prime for k values (of course, there are one or two exceptions like a small k-value). These equations yield lots of primes "compared". If one looks at P =+/- 61, they'll find that for k = 2 through 7 R is prime. Can anyone write a sieve for these numbers? Phil, maybe? I've search several thousand k values, but would love a sieve to be more efficient.

---Cletus Emmanuel

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• Your equations are a special form of the more general form 2^a +/- b*2^c +/- 1 Phil C. wrote a sieve base-10 of this form for me; you could ask him to write a
Message 2 of 2 , Jan 11 7:10 AM
Your equations are a special form of the more general form

2^a +/- b*2^c +/- 1

Phil C. wrote a sieve base-10 of this form for me;
you could ask him to write a sieve base-2 for you
or a variable base.
Why you assume that b (your P) must be prime for
the expression to be prime?

gr. rob

----- Original Message -----
From: Cletus Emmanuel
Sent: Monday, January 10, 2005 9:00 PM

Guys,
I've been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting ones so far are:

1. 4^k +/- 61*2^(k-1) - 1

2. 4^k +/- 139*2^(k-1) - 1

If P is not prime, then R would not be prime for k values (of course, there are one or two exceptions like a small k-value). These equations yield lots of primes "compared". If one looks at P =+/- 61, they'll find that for k = 2 through 7 R is prime. Can anyone write a sieve for these numbers? Phil, maybe? I've search several thousand k values, but would love a sieve to be more efficient.

---Cletus Emmanuel

---------------------------------
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Yahoo! Mail - 250MB free storage. Do more. Manage less.

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