Re: [math-fun] How often does every bit matter?
This provable Sierpinski number 2131043 is (1) prime, (2) "every bit matters" including leading 0s, i.e. if any bit in its binary expression is altered, the result is nonprime. Is it the least such number? It might be possible to prove that by showing that all prime numbers below 2131043 fail to have the "every bit matters including leading zeros" property...
James's link posted earlier today addresses this question: Re the Sierpinski problem this link: http://www.prothsearch.net/sierp.html may be of interest, especially the March 2013 update. The conjectured smallest prime Sierpinski number is 271129. - Scott
This provable Sierpinski number 2131043 is (1) prime, (2) "every bit matters" including leading 0s, i.e. if any bit in its binary expression is altered, the result is nonprime.
Is it the least such number? It might be possible to prove that by showing that all prime numbers below 2131043 fail to have the "every bit matters including leading zeros" property...
On 4/2/13, Warren D Smith <warren.wds@gmail.com> wrote:
This provable Sierpinski number 2131043 is (1) prime, (2) "every bit matters" including leading 0s, i.e. if any bit in its binary expression is altered, the result is nonprime.
Is it the least such number? It might be possible to prove that by showing that all prime numbers below 2131043 fail to have the "every bit matters including leading zeros" property...
--sorry! 2131043 - 2^6 is prime. Let me try again: This provable Sierpinski number 2131099 = 1000001000010010011011 binary is (1) prime, (2) "every bit matters" including leading 0s, i.e. if any bit in its binary expression is altered, the result is nonprime. Is it the least such number? It might be possible to prove that by showing that all prime numbers below 2131099 fail to have the "every bit matters including leading zeros" property... -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
participants (2)
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Huddleston, Scott -
Warren D Smith