Why NeRDs_360360?

paulunderwood · 2014-02-03, 04:49

Why did I choose 10^360360-10^k-1?

360360 = 2*2*2*3*3*5*7*11*13

For small primes p, 10^((p-1)*a)==1 (mod p), and so 10^360360-10^k-1 is not divisible by p. Consequently, after sieving, there is about 15% of the range left and we expect to find about 3 primes in the provable range k=90090-360360.

Batalov · 2014-02-03, 08:19

It would have been better to chose a>1290000*log₁₀2 for 10^a-10^k-1. With a=360360, the found primes will be swept away in about a year by the TwinGen-ial deluge. a=17#, perhaps?

Thomas11 · 2014-02-03, 08:33

Quote:

Originally Posted by paulunderwood

Consequently, after sieving, there is about 15% of the range left and we expect to find about 3 primes in the provable range k=90090-360360.

What's the total number of candidates left after sieving?

paulunderwood · 2014-02-03, 17:08

42320 candidates were left in the range 90000-360360.

Chuck Lasher is crunching 3/19 of this. Thomas, you are crunching 1/19. I crunched some. The rest was put up, ready for others to crunch -- 1 or 2 weeks per file folks.

paulunderwood · 2014-02-03, 17:10

Quote:

Originally Posted by Batalov

It would have been better to chose a>1290000*log₁₀2 for 10^a-10^k-1. With a=360360, the found primes will be swept away in about a year by the TwinGen-ial deluge. a=17#, perhaps?

These may be "swept away" from the top5000, but they should stay on the near-repdigit table.

I have exponents 388080 and 471240 sieved.

2014-02-03, 04:49	#1
paulunderwood Sep 2002 Database er0rr 118F₁₆ Posts	Why NeRDs_360360? Why did I choose 10^360360-10^k-1? 360360 = 22233571113 For small primes p, 10^((p-1)*a)==1 (mod p), and so 10^360360-10^k-1 is not divisible by p. Consequently, after sieving, there is about 15% of the range left and we expect to find about 3 primes in the provable range k=90090-360360.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
NeRDs_360360 reservations	paulunderwood	NeRDs	16	2014-11-24 08:32

2014-02-03, 08:19	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²×5×503 Posts	It would have been better to chose a>1290000*log₁₀2 for 10^a-10^k-1. With a=360360, the found primes will be swept away in about a year by the TwinGen-ial deluge. a=17#, perhaps?

2014-02-03, 17:08	#4
paulunderwood Sep 2002 Database er0rr 5·29·31 Posts	42320 candidates were left in the range 90000-360360. Chuck Lasher is crunching 3/19 of this. Thomas, you are crunching 1/19. I crunched some. The rest was put up, ready for others to crunch -- 1 or 2 weeks per file folks.