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#1 Re: This is Cool » Max Number of Consecutive Primes » 2015-01-23 11:38:04

Dear danaj, is it possible to run a program that you wrote using gpu processors with thousands of core doing the calculation? I am upgrading my computing power to mini-supercomputer using nvidia processors. It would be a great thing to find any series of in tens or perhaps near hundreds long series. If they don't exist then we can conjecture there would be no series longer than max number found so far.

#3 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-31 12:41:31

Thanks danaj for the input. Can you list the 10 consecutive primes. Thanks again for the script.

#4 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-30 17:48:07

Thanks danaj..the idea is to get all the Pr as prime with the sequential prime-th (i.e. s). Mathematica uses PrimeQ, a good primality algorithm for small primes, for larger prime you can use provableprimeQ which verifies the number to be prime. This is why it takes so long and if your computer is slow it could take months. I am trying to get longer series, perhaps up to 40 consecutive primes. So far, 8 is the largest.

#5 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-30 12:43:17

Dear Danaj can you list down the primes of 8 consecutive from your calculation? I am using mathematica and it is a bit slow. Mathematica got primality algorithm to verify the numbers, perhaps that makes it so slow. Anyway, thanks for the script, I am looking for a longer prime consecutive with the inputs.

#6 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-30 05:28:44

Just found another 8 consecutive prime for range 23,000,000<prime-th <24,000,000

#7 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-27 01:41:06

No apparent result bigger than 8 consecutive primes for Prime-th up to 20,000,000 for Pr=34+3s

#8 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-21 00:56:06

The max number of consecutive primes for Pr=34+3s is 8 (s<13,500,000)
For Pr=34+3s

Prime-th{13155307, 13155308, 13155309, 13155310, 13155311, 13155312, 13155313, 13155314}=s={239878543, 239878571, 239878579, 239878603, 239878621, 239878649, 239878663,
239878673}
Pr={719635663, 719635747, 719635771, 719635843, 719635897, 719635981, 719636023, 719636053} Consecutive Primes

#9 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-13 23:14:52

Another Primes for For Pr=34+3s (7 consecutive)

Prime-th{10654019, 10654020, 10654021, 10654022, 10654023, 10654024, 10654025}=s={191885429, 191885471, 191885483, 191885509, 191885539, 191885543, 191885563}
Pr={575656321, 575656447, 575656483, 575656561, 575656651, 575656663, 575656723} Consecutive Primes

#10 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-12 01:32:59

The max number of consecutive primes for s<10,000,000 still 7.

#11 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-09 15:54:32

I think there would be an infinite max numbers of consecutive primes as s goes to infinity.

#12 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-09 15:52:47

For Pr=34+3s

Prime-th{3036055, 3036056, 3036057, 3036058, 3036059, 3036060, 3036061}=s={50619193, 50619199, 50619221, 50619223, 50619229, 50619269, 50619271}
Pr={151857613, 151857631, 151857697, 151857703, 151857721, 151857841, 151857847} Consecutive Primes

#13 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-09 13:16:39

I have found 7 consecutive primes at higher s, could be more.

#14 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-08 20:22:29

There are plenty of four consecutive primes. Setting s to non-primes would make a single consecutive prime very rare or non-existence.

#15 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-07 16:12:40

Smallest solution for

s=1373th Prime{ 11369}, Pr=34141
s=1374th Prime {11383}, Pr=34183
s=1375th Prime {11393}, Pr=34213
s=1376th Prime {11399}, Pr=34231
s=1377th Prime {11411}, Pr=34267
s=1378th Prime {11423}, Pr=34303

#16 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-07 14:08:52

It seems for max consecutive primes for all n and s is 6.

#17 Re: This is Cool » Max Number of Consecutive Primes » 2014-12-07 05:08:28

For n=6

Max number of consecutive primes is 6 for s<1,500,000

#18 This is Cool » Max Number of Consecutive Primes » 2014-12-07 05:04:48

Stangerzv
Replies: 21

Consider this equation.

Where n is an even number, (n-1) should be prime and

is a consecutive Prime and s is a constant (also a prime).

Let n=4, yields


So far, the max number of consecutive prime formed is 6 for s<1,000,000

#20 Re: This is Cool » My New Twin Prime Numbers » 2014-10-31 05:00:04

Just wondering, could Ps be prime for composite Pt?

#21 Re: This is Cool » My New Twin Prime Numbers » 2014-10-26 12:15:24

Dear hemiboso

The twin primes we are talking about here are not the regular twin primes (i.e. with a gap of 2) but the prime numbers with a gap of +-n(number of primes used in the calculation as gap). Anyway, thanks for the insight.

#22 Re: This is Cool » My New Twin Prime Numbers » 2014-10-23 22:59:45

Dear danaj

Thanks for the insight, if I got plenty of free time surely I would do it.

To hemiboso, thanks for the input. It seems interesting.

#23 Re: This is Cool » My New Twin Prime Numbers » 2014-10-20 12:06:54

Thanks danaj

I think having a computer with GPU processing units (NVIDIA Tesla) would make it faster due to the fact it has thousand cores per GPU. I am still working on building one with multiple GPUs, got to wait until the GPU price going down after sometimes.

#24 Re: This is Cool » My New Twin Prime Numbers » 2014-10-18 22:57:44

Dear bobbym

Thanks for the info. I think I need to upgrade my computing power to do the job.

#25 Re: This is Cool » My New Twin Prime Numbers » 2014-10-18 00:54:53

Anybody knows how to run the primality test using AKS? Here the AKS article http://en.wikipedia.org/wiki/AKS_primality_test#History_and_running_time (I need for dummies instruction). I have ran ProvablePrimeQ[n] on the mathematica and even after more than a month still couldn't get the answer and it crashed my computer after sometimes. I need to make sure the primes here are true (especially for the large numbers).

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