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Perfect Primes:

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

The list is given as follows:

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

Smallest solution for Pt=4, when n=3

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

Would there be primes at n=48?

From calculation n=48 would only give one prime

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;

Twin Prime of Alternate Components, consider this equation:

Where

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