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#2 Re: This is Cool » My New Twin Prime Numbers » 2015-07-19 22:15:31

There are so far 3 groups of primes for consecutive power when n=3.

The list is given as follows:

 



#3 Re: This is Cool » My New Twin Prime Numbers » 2015-07-15 03:29:38

For larger value of primes, it seems that the value of n is always divisible by 3. Unless a counterexample is found.

#4 Re: This is Cool » My New Twin Prime Numbers » 2015-07-11 16:20:34

It is quite amazing to find out that the plus-minus n is always having a cycle of digital roots of 2,4,3,6 or 9.

#5 Re: This is Cool » My New Twin Prime Numbers » 2015-07-04 02:26:45

Thanks for the calculation. I do believe in the future the calculation time for ProvablePrimeQ would be smaller as the computing power is getting more powerful. I was using a supercomputer with a cluster of 2000 CPUs in the late 90s and it took sometimes up to 4 months to complete a finite element analysis of a small section of turbine jet engine component. Now, a single GPU like NVDIA tesla comprises of thousand cores in a single unit of processor would make as if you are having a supercomputer at home. However, as the computing power getting faster the prime number is also getting larger and limitless. So back to the square one:)

#6 Re: This is Cool » My New Twin Prime Numbers » 2015-06-29 21:38:47

Dear Danaj, thanks for the calculation. Have you checked the prime with prime provable algorithm like in the mathematica?

#7 Re: This is Cool » My New Twin Prime Numbers » 2015-06-28 06:39:28

Dear danaj, that's not a solution because n is the number of terms used. Your equation uses n=3 and shouldn't be 57.

#8 Re: This is Cool » My New Twin Prime Numbers » 2015-06-27 10:09:59

For n<25, no apparent primes for Pt=5

For n<25, no apparent primes for Pt=6

For n<25, no apparent primes for Pt=7

#9 Re: This is Cool » My New Twin Prime Numbers » 2015-06-24 01:31:26

Smallest solution for Pt=4, when n=3


#10 Re: This is Cool » My New Twin Prime Numbers » 2015-06-22 07:07:45

Smallest solution for Pt=3, when n=2


Next prime when n=4


Next prime when n=6


Next prime when n=9


Next prime when n=15


#11 Re: This is Cool » My New Twin Prime Numbers » 2015-06-22 04:44:26

Would there be primes at n=48?

From calculation n=48 would only give one prime

#12 Re: This is Cool » My New Twin Prime Numbers » 2015-06-22 04:20:41

Smallest solution for Pt=2, when n=2;


Next solution, when Pt=2 and n=3;


Next solution, when Pt=2 and n=6;


Next solution, when Pt=2 and n=12;


Next solution, when Pt=2 and n=24;


#13 Re: This is Cool » My New Twin Prime Numbers » 2015-06-22 04:16:14

Twin Prime of Alternate Components, consider this equation:

Where

#14 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.

#16 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.

#17 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.

#18 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.

#19 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

#20 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

#21 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

#22 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

#23 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.

#24 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.

#25 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

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