Bases 251-500 reservations/statuses/primes

[gd_barnes]

Originally Posted by appeldorff

Just checking in on my reservation:

I have just crossed the n=24000 mark. Looks like I'm finally reaching the end

I'm not entirely sure about how many primes i've found since my last update @ n=15000 but I'll count whenever I'm done with the range.
One thing i can tell however is that there will be less than half the original candidates remaining (Currently have 273 candidates remaining out of 547).

An impressive amount of work. Thanks for the update. I'm always personally interested in the 2^q-1 bases so I'll be curious as to what remains when you're through.


Gary

[gd_barnes]

Ian,

In your recent batch, you showed R354 with k=22 & 66 remaining and R394 with k=141 remaining but you also had primes for them in your files so they should have been eliminated.

The error seems to be on primes that were found for n>2500 because your # of found primes was also off by the same amount.

I have corrected the posts. I'll go back and check some previous posts for the same situation.

Edit: I found 2 more back prior to post 900: You showed R294 with k=60 remaining and R334 with k=26 remaining, both of which had primes.

I went all the way back to post 800 and those were the only problems of that nature that I found. It appears that the error just came up more recently where you had bases with more k's remaining in addition to algebraic k's.

Just a heads up...The web pages are now updated to correct the situation.


Gary

[MyDogBuster]

Just a heads up...The web pages are now updated to correct the situation.

Aha, I found an error in a script I use to shuffle stuff from remaining to prime. Bad testing. Sorry

It's a new script so the damage should just be to those 4 bases.

[MyDogBuster]

More algebraic factors

Reserving Riesel base 474

[MyDogBuster]

Riesel Base 424
Conjectured k = 69
Covering Set = 5, 17
Trivial Factors k == 1 mod 3(3) and k == 1 mod 47(47)

Found Primes: 40k's File attached

Remaining k's: Tested to n=25K
9*424^n-1 <------ Proven composite by partial algebraic factors
18*424^n-1
21*424^n-1
44*424^n-1

Trivial Factor Eliminations: 23k's

Base Released

[MyDogBuster]

Riesel Base 429
Conjectured k = 44
Covering Set = 5, 43
Trivial Factors k == 1 mod 2(2)

Found Primes: 20k's File attached

Remaining k's:
4*429^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

[MyDogBuster]

Riesel Base 439
Conjectured k = 144
Covering Set = 5, 11
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 73(73)

Found Primes: 42k's File attached

Remaining k's: Tested to n=25K
44*439^n-1
96*439^n-1
120*439^n-1
122*439^n-1

Trivial Factor Eliminations: 25k's

Base Released

[MyDogBuster]

Riesel Base 444
Conjectured k = 179
Covering Set = 5, 89
Trivial Factors k == 1 mod 443(443)

Found Primes: 163k's File attached

Remaining k's: Tested to n=25K
4*444^n-1 <------ Proven composite by partial algebraic factors
9*444^n-1 <------ Proven composite by partial algebraic factors
11*444^n-1
26*444^n-1
36*444^n-1
49*444^n-1 <------ Proven composite by partial algebraic factors
64*444^n-1 <------ Proven composite by partial algebraic factors
74*444^n-1
96*444^n-1
111*444^n-1
114*444^n-1
123*444^n-1
144*444^n-1 <------ Proven composite by partial algebraic factors
169*444^n-1 <------ Proven composite by partial algebraic factors

Base Released

[MyDogBuster]

Riesel Base 459
Conjectured k = 24
Covering Set = 5, 23
Trivial Factors k == 1 mod 2(2) and k == 1 mod 229(229)

Found Primes: 10k's File attached

Remaining k's:
4*459^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

[rogue]

Originally Posted by MyDogBuster

4*444^n-1 <------ Proven composite by partial algebraic factors
9*444^n-1 <------ Proven composite by partial algebraic factors
49*444^n-1 <------ Proven composite by partial algebraic factors
64*444^n-1 <------ Proven composite by partial algebraic factors
144*444^n-1 <------ Proven composite by partial algebraic factors
169*444^n-1 <------ Proven composite by partial algebraic factors

I have a question that I hope someone could answer regarding algebraic factorizations. I understand where you can find one (easily) if n is even, but what is the algebraic factorization if n is odd or when n is prime?

[Mini-Geek]

Originally Posted by rogue

I have a question that I hope someone could answer regarding algebraic factorizations. I understand where you can find one (easily) if n is even, but what is the algebraic factorization if n is odd or when n is prime?

From looking at the lists in the FactorDB, I'm inclined to think the odd n's are eliminated due to a factor of 5. Since I fail to see a mathematical reason for all this, I'll just leave it at that.