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| Richard L. Peterson... |
 Posted: Sat Oct 31, 2009 4:23 pm |
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sum of 2 squares and at least 1 prime that is
not the sum of 2 squares between every 2
postive squares. That is:[1. 2;3 4] [4. 5;7 9]
[9. 11;13 16] [16. 17;19 25].....
[169. 173;179 196] [196. 197;211 225] etc.
Has this been proven? Thanks. |
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| Gerry... |
| Posted: Sat Oct 31, 2009 7:12 pm |
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On Nov 1, 1:23 pm, "Richard L. Peterson" <rl_p... at (no spam) yahoo.com> wrote:
[quote]sum of 2 squares and at least 1 prime that is
not the sum of 2 squares between every 2
postive squares. That is:[1. 2;3 4] [4. 5;7 9]
[9. 11;13 16] [16. 17;19 25].....
[169. 173;179 196] [196. 197;211 225] etc.
Has this been proven? Thanks.
[/quote]
An odd prime is the sum of two squares if it's 1 more
that a multiple of 4; it's not a sum of two squares
if it's 1 less than a multiple of 4. So you're asking about
there being both a prime that's 1 mod 4 and a prime
that's -1 mod 4 between two squares (and the exceptional
case involving the prime 2).
Well, it's a notorious open problem to prove that there's
always a prime between two consecutive squares. Your
question is surely open.
--
GM |
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| Richard L. Peterson... |
| Posted: Fri Nov 06, 2009 1:21 pm |
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[quote]On Nov 1, 1:23Â pm, "Richard L. Peterson"
rl_p... at (no spam) yahoo.com> wrote:
sum of 2 squares and at least 1 prime that is
not the sum of 2 squares between every 2
postive squares. That is:[1. 2;3 Â 4] [4. 5;7 Â 9]
[9. 11;13 Â 16] [16. Â 17;19 Â 25].....
[169. Â 173;179 Â 196] [196. Â 197;211 Â 225] etc.
Has this been proven? Thanks.
An odd prime is the sum of two squares if it's 1 more
that a multiple of 4; it's not a sum of two squares
if it's 1 less than a multiple of 4. So you're asking
about
there being both a prime that's 1 mod 4 and a prime
that's -1 mod 4 between two squares (and the
exceptional
case involving the prime 2).
Well, it's a notorious open problem to prove that
there's
always a prime between two consecutive squares. Your
question is surely open.
--
GM
[/quote]
Thanks for the information! It
does seem that the "notorious open"
conjecture could be true even if my
conjecture were false |
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