EUREKA!!!!!!!!!!!!!!!!!!!!!!!!

[Max A.]

If I understood you correctly, you want to win the EFF prize for aprime with 10^7 digits by finding a number of that size such that ithas a prime number nearby (e.g., "3 last digits varying").
I see two problems with your arguments:
First, it is not clear at all why only 3 last digits will be varying.OK, you've got some small examples supporting this claim but examplesdo not prove anything. Have you heard of the Law of small numbers?http://mathworld.wolfram.com/StrongLawofSmallNumbers.html
Second, even if you are correct (or lucky) to catch a prime numberwith 10^7 digits, how you are going to prove that it is prime? What is"modified Wilson-Lehmer" you are referring to? Generic deterministicprimality tests are not fast enough for the numbers of that size.There are fast primality tests but they are probabilistic, meaningthat they cannot substitute a proof of primality (required by EFF).
Max

On 12/16/06, Artur <grafix at csl.pl> wrote:> Dear Seqfans,> Is following optimalization problem> Finding basis of counting system such that time reaching 10 000 000 digits> prime by my procedure will be shortest.> Formula will be follwing for my previous sequence will be:> If we take counting system basis 100 3 last digits varying (see bellow)> For my previous system if we go from a(odd) to a(even) one digit varying.> Probababilty of success (that we find prime) is 1/5 if we go from a(even)> to a(odd) two last digits varying and in this case probabilty is 1/50. To> reaching prime 10 000 000 digits we need 5 000 000 checkings with> probability 1/5 and 5 000 000 with probability 1/50 together> 5000000*5+5000000*50 = 275000000 steps. Now we take to counting that time> of checking that number is prime or not by modified Wilson-Lehmer> algorithm is log(number of digits). My question is which counting system> will be the quickest one.> BEST WISHES> ARTUR>>>>> %I A000001> %S A000001 !
2, 199, 19891, 1989077, 198907679, 19890767893, 1989076789283,> 198907678928279, 19890767892827873, 1989076789282787297,> 198907678928278729697, 19890767892827872969661, 1989076789282787296966091,> 198907678928278729696609039, 19890767892827872969660903813,> 1989076789282787296966090381249, 198907678928278729696609038124829,> 19890767892827872969660903812482509, 1989076789282787296966090381248250849,> 198907678928278729696609038124825084813,> 19890767892827872969660903812482508481211,> 1989076789282787296966090381248250848120823,> 198907678928278729696609038124825084812082207,> 19890767892827872969660903812482508481208220559,> 1989076789282787296966090381248250848120822055831,> 198907678928278729696609038124825084812082205583091,> 19890767892827872969660903812482508481208220558309043,> 1989076789282787296966090381248250848120822055830904249,> 198907678928278729696609038124825084812082205583090424757,> 19890767892827872969660903812482508481208220558309042475663> %N A000001 Bi!
ggest primes <100*a[n-1] a[1]=2> %F A000001 a(n) = 10*a(n-1)>!
 %Y A000001 A006902,A040016,A120031-A120041> %O A000001 1> %K A000001 ,nonn,> %A A000001 Artur Jasinski (grafix at csl.pl), Dec 16 2006> Dnia 16-12-2006 o 20:16:13 Artur <grafix at csl.pl> napisał(a):>> > Dear Jonathan and Others,> > Binary system isn't as effective as decimal because 5 or 6 last digits> > varying> > %I A000001> > %S A000001> > 10,11,101,111,1101,10111,10101,1010011,10100011,100111101,1001110111,> > 10011101011,100111000111,1001110001011,10011011110101,100110111100001,> > 1001101110111101,10011011101010011,100110111010011101,1001101110100011111,> > 10011011101000111011,100110111010001101101,1001101110100010111111,> > 10011011101000101110101,100110111010001011010111,1001101110100010110101011,> > 10011011101000101101000001,100110111010001011001110011,> > 100110111010001011011100001,10011011101000101100110111001,> > 100110111010001011001101010111,1001101110100010110011010010111,> > 10011011101000101100110100011001,100110111010001011001101000101011,> > 10011011101000!
10110011010001000001,10011011101000101100110100001111001,> > 100110111010001011001101000011101111,1001101110100010110011010000110111101,> > 10011011101000101100110100001101011011,100110111010001011001101000011010110101> > %N A000001 Biggest primes writen in binary system <2*a[n-1] a[1]=2> > %C A000001 These sequence visualized Chebyshev low that between n and 2n> > existed minimum 1 prime> > %F A000001 a(n) = 2*a(n-1)> > %Y A000001 A006902,A040016,A120031-A120041> > %O A000001 1> > %K A000001 ,nonn,> > %A A000001 Artur Jasinski (grafix at csl.pl), Dec 16 2006> >> > Dnia 16-12-2006 o 18:12:23 Jonathan Post <jvospost3 at gmail.com>> > napisał(a):> >> >> "Chebychev said it and I'll say it again:> >> There's always a prime between n and 2n."> >>> >> I skipped the attribution in A118909.*> >> *> >> Joseph Louis François Bertrand [1822-1900] was the Paris professor who> >> made> >> the conjecture, proved by Chenychev in 1850. I have heard that It> >> appears> >> that Nat Fine wrote th!
is couplet in honor of Paul Erdos.> >>> >> Jasinski said it, !
and emailed again:> >> There's always a prime between n and 10n.> >>> >> "ten" rhymes with "n."  This is as great an advance in mathematical> >> poetry> >> as any sequence containing "14" is to sonnets.  Or, more to the point,> >> as> >> the fact that the number of syllables in a haiku is prime.> >>> >> I'm nearly the last person to criticize anyone who submits a base> >> sequence,> >> or a sequence involving primes. But when I do, I know it to be a base> >> sequence, and endeavor to submit the more generalized sequence of> >> antidiagonals of the array of such a sequence over all natural number> >> bases.> >>> >> Sometimes generalization sheds new light on a problem. Grothendieck, for> >> instance, as a master of that, before he turned his mind to politics. If> >> there is an enlightening generalization that moves beyond the> >> arbitrariness> >> on decimal base, I'd be pleased to see it.> >>> >> No disrespect to Jasinski.  I also have made the mistake of> >> egotistically>!
 >> proposing to name something after myself (a la Donald Trump), and over> >> premature exclamation marks, not symbolizing factorials, out of> >> excitement> >> and enthusiam. Also, sometimes I like the sequences by this gentleman,> >> as> >> indicated by A113914 and its ilk.> >>> >> In this holiday season, perhaps it is best to lean towards tolerance,> >> charity, forgiveness, and kindness.> >>> >> -- Jonathan Vos Post> >>> >> On 12/16/06, Hans Havermann <pxp at rogers.com> wrote:> >>>> >>> Antti Karttunen asked:> >>>> >>> So, please tell us, what is the ground-breaking idea in your primes> >>> below?> >>>> >>>> >>> 17989, 179849, 1798487, 17984833, 179848309, 1798483067,> >>> 17984830667, 179848306667, 1798483066669, 17984830666651,> >>> 179848306666507,> >>> ...> >>>> >>>> >>> I can at least verify that:> >>>> >>> a(1) = 17989> >>> a(n) = PreviousPrime[10*a(n-1)]> >>>> >>> I hope there's more to it than that. ;)> >>>> >>>> >> >> >> > __________ NOD32 Informacje 1924 (200612!
15) __________> >> > Wiadomosc zostala sprawdzona przez Syste!
m Antywirusowy NOD32> > http://www.nod32.com lub http://www.nod32.pl> >>>>