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Search: Posts Made By: NHoodMath
Forum: Conjectures 'R Us 2021-08-28, 21:44
Replies: 135
Views: 37,717
Posted By NHoodMath
It is actually quite common for a base to have...

It is actually quite common for a base to have the same CK on both sides due to how the math behind the CK works (I'll outline the simplest case). Say for a given base b that primes p and q > 2...
Forum: Conjectures 'R Us 2021-08-24, 00:09
Replies: 135
Views: 37,717
Posted By NHoodMath
I actually quit on this in January, it reached...

I actually quit on this in January, it reached 30K with no new primes, still 7 k's remaining (22, 32, 74, 98, 212, 254, 332), highest prime found was for k=242 at n=13212.
Forum: And now for something completely different 2021-05-23, 18:28
Replies: 294
Views: 52,807
Posted By NHoodMath
Base 180 complete to n=30K No primes found-...

Base 180 complete to n=30K

No primes found- Base Released

Results file attached

This base fell into a very large primeless void and never came out...
Forum: And now for something completely different 2021-05-19, 22:45
Replies: 294
Views: 52,807
Posted By NHoodMath
Base 180 reached n=20K yesterday, just reached...

Base 180 reached n=20K yesterday, just reached 21K, no primes for n=10K-21K, continuing

base 180 is very low weight base (8th lowest weight of all bases <3000) so I wasn't really expecting primes.
Forum: And now for something completely different 2021-05-17, 01:43
Replies: 294
Views: 52,807
Posted By NHoodMath
Releasing 2970 Reserving CK180

Releasing 2970

Reserving CK180
Forum: And now for something completely different 2021-05-15, 06:59
Replies: 294
Views: 52,807
Posted By NHoodMath
yes Testing complete to 10K, no other primes

yes

Testing complete to 10K, no other primes
Forum: And now for something completely different 2021-05-15, 05:01
Replies: 294
Views: 52,807
Posted By NHoodMath
base 2970

Reserving base 2970 to n=10K

Currently have 1 prime to report to go toward the project goals:
(2970^2993+1)^2-2
Tested up to 8.4K currently with no other primes.
Forum: Miscellaneous Math 2021-02-07, 15:55
Replies: 17
Views: 1,947
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: 135
Views: 37,717
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: 1,191
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: 1,357
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: 1,106
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: 1,106
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: 1,138
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: 19,995
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: 19,995
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: 3,950
Views: 316,854
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: 135
Views: 37,717
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: 3,950
Views: 316,854
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: 135
Views: 37,717
Posted By NHoodMath
next prp

189*2020^20878+1
363*2020^22046+1
Forum: Conjectures 'R Us 2020-01-19, 19:08
Replies: 135
Views: 37,717
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: 135
Views: 37,717
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: 135
Views: 37,717
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: 3,950
Views: 316,854
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: 135
Views: 37,717
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...
Showing results 1 to 25 of 35

 
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