January 2007 - mathfun@mailman.xmission.com

[math-fun] Question about primes
by Daniel Asimov 09 Jan '07

09 Jan '07

Is it known whether for each prime p there exists at least one prime q such that pq + 1 is prime? --Dan

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[math-fun] First, second, third, fourth... absolute differences
by Eric Angelini 08 Jan '07

08 Jan '07

Hello Math-Fun, Is this of interest? http://www.cetteadressecomportecinquantesignes.com/1234diff.htm Best, É.

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Re: [math-fun] Car Talk and prime numbers
by Phil Carmody 08 Jan '07

08 Jan '07

From: "Michael Kleber" <michael.kleber(a)gmail.com> > > Phil Carmody wrote: > > > http://people.brandeis.edu/~kleber/temp/deletable.html > > """ > > Question: Why do prime bases (in red) seem to have many fewer deletable > primes > > than composite bases? > > """ > > > > A much simpler, in fact trivial, question is: > > Why do odd bases seem to have many fewer deletable primes than even ones? > > You're right, that does look like the right question to ask. > When you say this is a trivial question, do you mean you > know an answer, or just that it is easier to ask? Yes. <stifles sniggering> Think of the problem of growing deletable primes by insertion, as in my script. If we have deletable prime P in base B and N digits in length, how many ways, ignoring duplication, are there to create a number one digit longer? If B was odd, how many of those ways yield an even number? And how many ways if B was even? Tada! Bob's your auntie's live-in lover. Wnen it comes to density of primes, is almost always explainable in terms of small prime divisors. This is no exception. Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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Re: [math-fun] Car Talk and prime numbers
by Phil Carmody 08 Jan '07

08 Jan '07

From: "Michael Kleber" > Subject: Re: [math-fun] Car Talk and prime numbers > > Heh: when was the last time someone responded to one of > NJAS's questions by saying the equivalent of "See A096237"? > > We (math-fun) discussed this in Feb-Mar 2003, eventually > calling them "deletable primes," terminology which I think > was preexisting. There seem to be infinitely many of them. > > At the time, we came across one surprising observation, > which (in the way of the web) is still sitting here: > http://people.brandeis.edu/~kleber/temp/deletable.html """ Question: Why do prime bases (in red) seem to have many fewer deletable primes than composite bases? """ A much simpler, in fact trivial, question is: Why do odd bases seem to have many fewer deletable primes than even ones? Then I'd posit that the real question is commuted to: Do prime bases have significantly fewer deletable primes than composite odd bases? Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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RE: [math-fun] First, second, third, fourth... absolute differences
by Schroeppel, Richard 08 Jan '07

08 Jan '07

Although I approve of putting long computations out of the message stream, there's an unfortunate side effect: It means this never gets into our recorded archive. Someone who's looking over old messages next year won't be able to learn much from URLs that have evaporated. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov(a)mailman.xmission.com [mailto:math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com] On Behalf Of Eric Angelini Sent: Monday, January 08, 2007 12:02 PM To: math-fun Subject: [math-fun] First, second, third, fourth... absolute differences Hello Math-Fun, Is this of interest? http://www.cetteadressecomportecinquantesignes.com/1234diff.htm Best, É. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Re: Car Talk and prime numbers
by N. J. A. Sloane 08 Jan '07

08 Jan '07

I asked this list on Saturday about deletable primes. Thanks to everyone who replied. But no one answered my specific question about the largest known deletable prime, so I'm adding these two sequences to the OEIS. Maybe someone would like to extend them! (I will also update them with references to various links that people sent me.) Neil %I A125589 %S A125589 2,13,103,1013,10039 %N A125589 Smallest n-digit base-10 deletable prime. %C A125589 A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b. %C A125589 Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed. %Y A125589 Cf. A080608, A096246, A125590. %K A125589 nonn,base,more,new %O A125589 1,1 %A A125589 njas, Jan 07 2007 %I A125590 %S A125590 7,97,997,9973,99929 %N A125590 Largest n-digit base-10 deletable prime. %e A125590 99929 -> 9929 -> 929 -> 29 -> 2. %Y A125590 Cf. A080608, A096246, A125589. %K A125590 nonn,base,more,new %O A125590 1,1 %A A125590 njas, Jan 07 2007

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[math-fun] Re: Car Talk and prime numbers
by Phil Carmody 06 Jan '07

06 Jan '07

[bcc: various places] From: Jud McCranie <j.mccranie(a)adelphia.net> > At 07:03 PM 1/6/2007, N. J. A. Sloane wrote: > > >This led me to wonder about the analogous question for primes. > >This must be well-studied. What's the largest prime known > >with property that you can repeatedly delete a digit (you get > >to choose which digit) and still have > >a prime, all the way down to the empty word? > > > I think this is the largest known: > http://primes.utm.edu/glossary/page.php?sort=DeletablePrime Tish pish. They're everywhere and trivial to grow. 2 23 223 1223 10223 102023 1020023 10200263 102002603 1020026303 10200226303 102002263031 1020002263031 10200022363031 102000223263031 1020000223263031 10200002232630131 102000022326301313 1020000222326301313 10200002223236301313 102000012223236301313 1020000122232363013013 10200000122232363013013 102000001222320363013013 1020000012223202363013013 10120000012223202363013013 101200000122232002363013013 1012000001222320023623013013 10120000001222320023623013013 101200000012022320023623013013 1012000000112022320023623013013 10120000001120223200236230130313 101200000011202023200236230130313 1012000000112020232002362301303813 10120000001120202320020362301303813 101200000011202023200203623013036813 1010200000011202023200203623013036813 10102000000112020213200203623013036813 101020000001120202103200203623013036813 1010200000011202002103200203623013036813 10102000000112020021032002036230130326813 101002000000112020021032002036230130326813 1010020000001012020021032002036230130326813 10100200000010120200210312002036230130326813 101002000000101202002103132002036230130326813 1010020000001012020020103132002036230130326813 10100200000010120200201031320002036230130326813 100100200000010120200201031320002036230130326813 1001002000000101202002010313200020362301303265813 10010020000001012020020103132000120362301303265813 100100200000010120200201031232000120362301303265813 1001002000000101202001201031232000120362301303265813 10010020000001012020012010312320001203623013032065813 100100020000001012020012010312320001203623013032065813 1001000200000010120200120103123200012036230138032065813 10010002000000101202001201031232000120362301380320765813 100100020000001012020012010312320001203062301380320765813 1001000200000010120200120103123200012030623013803207658163 10010002000000101202001201031232000120030623013803207658163 100100020000001012020012010312320001020030623013803207658163 1001000200000010120200120103123200010200306223013803207658163 10010002000000101202001200103123200010200306223013803207658163 100100020000001012020012001031232000102003062230138032076584163 1001000200000010120020012001031232000102003062230138032076584163 10010002000000101200200120010312320001020030622301038032076584163 100100020000001012002001200103123200010200306223201038032076584163 1001000200000010120020012001031232000102003062232010380372076584163 10010002000000101200200120010312302000102003062232010380372076584163 Which was about half a second of the following, utterly inefficient (it finds all possible (probable) primes before recursing) GP script: <<< lengthen(p, l) = local(n=listcreate(10*l+10), v=[], bot=p, cut=10^l, t, i); print(p);while(l>=0,t=(bot\cut)*cut;p+=9*t;bot-=t;for(i=0,9,listinsert(n,p+cut*i,length(n)+1));l--;cut\=10);n=listsort(n);for(i=1,length(n)-1,if(n[i+1]!=n[i]&&ispseudoprime(n[i+1]),v=concat(v,[n[i+1]])));v rlengthen(seed, len) = local(r=lengthen(seed,len), i, v=len); for(i=1,length(r),rlengthen(r[i],len+1));v rlengthen(2,1) >>> Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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[math-fun] Car Talk and prime numbers
by N. J. A. Sloane 06 Jan '07

06 Jan '07

Dear Funsters, The radio program Car Talk today was discussing the problem of finding the longest English word which has the property that you can repeatedly delete one letter and still have an English word, all the way until the empty word is left (the best solution mentioned had 11 letters). At each step you can choose which letter to delete. This led me to wonder about the analogous question for primes. This must be well-studied. What's the largest prime known with property that you can repeatedly delete a digit (you get to choose which digit) and still have a prime, all the way down to the empty word? I don't want to sign this.

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Re: [math-fun] Car Talk and prime numbers
by Jud McCranie 06 Jan '07

06 Jan '07

At 07:08 PM 1/6/2007, Jud McCranie wrote: >I think this is the largest known: >http://primes.utm.edu/glossary/page.php?sort=DeletablePrime Whoops, that was far from the largest known: http://primes.utm.edu/curios/page.php?curio_id=1420

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[math-fun] Q. about {0,1}-matrices.
by N. J. A. Sloane 05 Jan '07

05 Jan '07

Dear MathFun, SeqFans: Could anyone extend this sequence? %I A125587 %S A125587 1,4,68,5008 %N A125587 Call an n X n matrix robust if the top left i X i submatrix is invertible for all i = 1...n. Sequence gives number of n X n robust real {0,1}-matrices. %e A125587 a(2) = 4: %e A125587 10 10 11 11 %e A125587 01 11 01 10 %O A125587 1,2 %Y A125587 Cf. A125586. %K A125587 nonn,more %A A125587 njas and Vinay Vaishampayan (vinay(AT)research.att.com) Jan 05 2007 This "robust" property is relevant when doing an LU decomposition of a matrix, so it may have a more official name (besides "all principal submatrices are nonsingular", I mean). Neil

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