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I can do it even faster:) With a calculator!

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

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

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

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

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

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

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

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

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

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

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

For n=6

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

**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

Ok Got one solution for Pt=4

Just wondering, could Ps be prime for composite Pt?

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.

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.

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.

Dear bobbym

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