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

[Artur]

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 Biggest 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,
> 1001101110100010110011010001000001,10011011101000101100110100001111001,
> 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 this 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. ;)
>>>
>>>
>
>
>
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