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Old 2012-02-26, 16:29   #1
Arkadiusz
 
Dec 2009

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Default Highly composite polynomials.

"Other polynomials of this type include n^6 + 29450922301244534, which was discovered by Carmody in 2006 (Rivera) and is prime for 63693"
http://mathworld.wolfram.com/Prime-G...olynomial.html

Why did they not publish a better solution?
Why not 100000, 200000, ...?

Last fiddled with by ewmayer on 2013-02-17 at 20:02 Reason: grammar fixed at author request
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Old 2012-02-26, 16:50   #2
Arkadiusz
 
Dec 2009

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625567359447343581348856464285098545399036422015846188212576\
005216959264198326888770861800982403133642359585169933857500\
94682865830363609 291648
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Old 2012-02-27, 04:16   #3
axn
 
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Quote:
Originally Posted by Arkadiusz View Post
"Other polynomials of this type include n^6 + 29450922301244534, which was discovered by Carmody in 2006 (Rivera) and is prime for 63693"
http://mathworld.wolfram.com/Prime-G...olynomial.html

Why they did not publish a better solution?
Why not 100000, 200000, ...?
Why are 100000, 200000, ... better solutions?

Quote:
Originally Posted by Arkadiusz View Post
625567359447343581348856464285098545399036422015846188212576\
005216959264198326888770861800982403133642359585169933857500\
94682865830363609 291648
What is this supposed to represent?
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Old 2012-02-27, 05:01   #4
LaurV
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Quote:
Originally Posted by axn View Post
What is this supposed to represent?
I assume (from the page on mathworld linked by the OP) that the first number is a prime generated by the polynomial when x is substituted with the second (red) value. What is used for, no idea...

Last fiddled with by LaurV on 2012-02-27 at 05:04
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Old 2012-02-27, 05:22   #5
axn
 
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Quote:
Originally Posted by LaurV View Post
I assume (from the page on mathworld linked by the OP) that the first number is a prime generated by the polynomial when x is substituted with the second (red) value. What is used for, no idea...
That was my first thought -- but upon checking, the number isn't prime, isn't generated by the polynomial at all, and the index 291648 in the given polynomial doesn't generate a prime.

EDIT:- Figured it out. The generating polynomial is n^6+ 625567...63609 and its first prime is found at n=291648. Which is superficially better than the first polynomial, but, once you factor in the average size of the numbers generated, is relatively worse.

Last fiddled with by axn on 2012-02-27 at 05:28
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Old 2012-02-27, 14:11   #6
Arkadiusz
 
Dec 2009

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Quote:
Originally Posted by axn View Post
Which is superficially better than the first polynomial, but, once you factor in the average size of the numbers generated, is relatively worse.
Maybe we should find a qualification formula.
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