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Forum: Miscellaneous Math 2021-02-07, 15:55
Replies: 17
Views: 1,438
Posted By NHoodMath
Other closed form of the Hugo sequence and observations

There is a much simpler closed form for the Hugo Numbers than what has been posted by Hugo and the others, they are equal to:

(Sum from k=0 to k=(p-1)/2 of (Binomial(p, 2*k)*13^k))/2^(n-1)

It...
Forum: Conjectures 'R Us 2021-01-07, 22:44
Replies: 132
Views: 35,269
Posted By NHoodMath
I already had this one (R2021) searched to 13K,...

I already had this one (R2021) searched to 13K, going to 25K rn (BTW I did finish those 3 k's on S2020 to n=100K, no primes)
Forum: enzocreti 2020-02-17, 22:17
Replies: 7
Views: 1,136
Posted By NHoodMath
Certainly a low-weight sequence, but...

Certainly a low-weight sequence, but 5*(10^156-1)/9+360268786 is prime.
Forum: enzocreti 2020-02-13, 22:30
Replies: 3
Views: 1,183
Posted By NHoodMath
There is a mathematically rigorous way to analyze...

There is a mathematically rigorous way to analyze this.
Repunit numbers can also be written as numbers of the form (10^n-1)/9, with n a positive integer.
(10^21-1)/9 is the smallest repunit...
Forum: enzocreti 2020-02-13, 22:18
Replies: 6
559
Views: 879
Posted By NHoodMath
x^3-y^3=(x-y)(x^2+xy+y^2), so if x-y=1, then...

x^3-y^3=(x-y)(x^2+xy+y^2), so if x-y=1, then y=x-1 and the quadratic becomes x^2+x(x+-1)+(x-1)^2=x^2+x^2-x+x^2-2x+1=3x^2-3x+1, so if 3x^2-3x+1 is a Mersenne prime, then x^3-y^3 is also a Mersenne...
Forum: enzocreti 2020-02-13, 21:55
Replies: 6
559
Views: 879
Posted By NHoodMath
x^3+y^3=(x+y)(x^2-xy+y^2), so yes there are...

x^3+y^3=(x+y)(x^2-xy+y^2), so yes there are infinitely many numbers x and y such that x+y is divisible by 43, and thus x^3+y^3 as well by association.
Forum: enzocreti 2020-02-10, 23:39
Replies: 3
Views: 1,030
Posted By NHoodMath
Enzo, here is some relevant maths to what you...

Enzo, here is some relevant maths to what you have posted here:

The number 51, in your case, you were testing to see whether it was a quadratic residue (mod 163), that is, whether or not there is...
Forum: Conjectures 'R Us 2020-02-06, 03:17
Replies: 40
Views: 17,811
Posted By NHoodMath
Just as a note so if dannyridel is interested,...

Just as a note so if dannyridel is interested, use covering.exe for small CK (say k<2^32) and bigcovering.exe for larger CK than 2^32. There is a bug in the covering.exe program for k's greater than...
Forum: Conjectures 'R Us 2020-02-05, 22:51
Replies: 40
Views: 17,811
Posted By NHoodMath
Sweety's code appears to be brute-forcing the CK...

Sweety's code appears to be brute-forcing the CK search. Doing it rigorously requires advanced mathematics (modulo arithmetic, orders mod n, Chinese Remainder Theorem, sometimes quadratic, cubic...
Forum: Conjectures 'R Us 2020-02-02, 23:38
Replies: 3,857
Views: 289,239
Posted By NHoodMath
Just making sure you are aware that k values...

Just making sure you are aware that k values 2704, 61009, and 786615 can be eliminated from the conjecture, 2704 due to 52^2 and 541 on odd n, 786615 due to 15*229^2 and 541 on even n, and 61009 due...
Forum: Conjectures 'R Us 2020-02-01, 15:53
Replies: 132
Views: 35,269
Posted By NHoodMath
Sierp base 2020 complete to 25K. 21 k's at 10K -...

Sierp base 2020 complete to 25K. 21 k's at 10K - 6 k's found prime for 10K-25K = 15 k's remaining. Base released except k=12, 402, and 892. K's remaining:
12
138
255
259
291
390
402
430
471
Forum: Conjectures 'R Us 2020-01-31, 23:54
Replies: 3,857
Views: 289,239
Posted By NHoodMath
If you are using LLR, remove k's from testing by...

If you are using LLR, remove k's from testing by manually adding ks(k-value)=1 to llr.ini (ex ks1968=1 for k=1968 removal)
Forum: Conjectures 'R Us 2020-01-24, 23:11
Replies: 132
Views: 35,269
Posted By NHoodMath
next prp

189*2020^20878+1
363*2020^22046+1
Forum: Conjectures 'R Us 2020-01-19, 19:08
Replies: 132
Views: 35,269
Posted By NHoodMath
sweety, CRUS does not intend any work on k's > CK...

sweety, CRUS does not intend any work on k's > CK because the project's goal is simply to solve the 1st conjecture for each individual base. If k's > CK were included, decisions would have to be made...
Forum: Conjectures 'R Us 2020-01-18, 22:48
Replies: 132
Views: 35,269
Posted By NHoodMath
@sweety, R2048 has 2 k remaining, k=5 and k=11,...

@sweety, R2048 has 2 k remaining, k=5 and k=11, both searched to very high limits over n=4M base 2 after accounting for the Riesel Sieve effort. Most other bases on your list have more k's remaining,...
Forum: Conjectures 'R Us 2020-01-06, 22:19
Replies: 132
Views: 35,269
Posted By NHoodMath
next PRP 411*2020^14877+1 tested to 17.8K, 17...

next PRP
411*2020^14877+1
tested to 17.8K, 17 k's remain. I expect this to be done within the week
Forum: Conjectures 'R Us 2020-01-03, 18:36
Replies: 3,857
Views: 289,239
Posted By NHoodMath
624=16*39 624=4^2*39 Any k that is a square...

624=16*39
624=4^2*39
Any k that is a square times the leftover non-square part of the base (39) has algebraic factors for odd n. These sometimes combine with a trivial factor (in this case 5) to...
Forum: Conjectures 'R Us 2020-01-01, 14:33
Replies: 132
Views: 35,269
Posted By NHoodMath
I think base 2019 and 2017 were the most...

I think base 2019 and 2017 were the most thoroughly searched of the "year" bases. Lalera did his hard work on getting the Riesel side of 2019 to n=200K (!) and the Sierp side, if not already tested...
Forum: Conjectures 'R Us 2020-01-01, 06:28
Replies: 132
Views: 35,269
Posted By NHoodMath
Comparing k's remaining w/VBCurtis

Just to check if we have the same 59 k's remaining:
9, 32, 42, 99, 128, 156, 171, 207, 216, 261, 275, 317, 345, 419, 428, 429, 471, 473, 519, 563, 582, 657, 687, 704, 776, 786, 788, 872, 941, 1023,...
Forum: Conjectures 'R Us 2020-01-01, 06:17
Replies: 132
Views: 35,269
Posted By NHoodMath
You can go ahead and test 10K-25K or however far...

You can go ahead and test 10K-25K or however far you wish. I honestly want no more part in that base
Forum: Conjectures 'R Us 2019-12-31, 15:00
Replies: 132
Views: 35,269
Posted By NHoodMath
Find attached the 6915 candidate sequences for...

Find attached the 6915 candidate sequences for R2020 8K=10K to n=5G (102.2s/n)


Also, status update on yesterday's S2020 reservation:
Testing is at n=14676, 3 new primes found, 18 k's remain:...
Forum: Conjectures 'R Us 2019-12-31, 00:51
Replies: 132
Views: 35,269
Posted By NHoodMath
How long does a test of a 20000 digit long number...

How long does a test of a 20000 digit long number take on your computer @VBCurtis? That way I can judge optimal depth
Forum: Conjectures 'R Us 2019-12-30, 20:45
Replies: 132
Views: 35,269
Posted By NHoodMath
Reserving Sierp. base 2020 (all 21 k's) from...

Reserving Sierp. base 2020 (all 21 k's) from 10K-20K. (At 10K the testing was progressing at about n=1K/day) also, just ask if you want the k's remaining at n=10K for this one.

Anyone want all 62...
Forum: Conjectures 'R Us 2017-08-18, 22:14
Replies: 2,281
Views: 198,372
Posted By NHoodMath
R411

I am taking the whole base, Bitcoin.
Forum: Conjectures 'R Us 2017-08-18, 20:54
Replies: 2,281
Views: 198,372
Posted By NHoodMath
R411

I have started work on Riesel base 411, CK 60254. So far, I have tested K<15K to 2.5K and will post weekly updates as I progress toward 25K.
Showing results 1 to 25 of 28

 
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