Are Legendre symbols proven to be defective?

[Mini-Geek]

Originally Posted by Anonymous

Using the latest sr1sieve, I found that 2^3355584+1 is divisible by 5. I verified the factor with Pari/GP (which as far as I know uses plain old straight division, with no "shortcuts").

I did the same thing, for k=1-5 n=3355583 and checked all factors with Pari/GP.

[ColdFury]

Is this the same "friend" who had the radical compression technique?

[mdettweiler]

Originally Posted by Mini-Geek

I did the same thing, for k=1-5 n=3355583 and checked all factors with Pari/GP.

I deleted my message, because I thought I put the output into Pari/GP wrong...but on second thought, though, it looks like I did do it correctly. :whoops: Can a mod please bring back my message?

[paulunderwood]

? n=3355584;forprime(p=3,1000,if(Mod(2,p)^n+1==0,print(p)))
769

The Windows version of NewPGen will not let me stop a test with divisor less that 1000 nor log divisors less than 2^32. I challenge jasong and his friends to reproduce their divisor of 2 by NewPGen

[R.D. Silverman]

Originally Posted by ewmayer

Yes, Bob is dating himself, but Bob has an admirably reckless disregard for fashion and fads. The rest of us, slaves to hipster trends as we are, probably would prefer more up-to-date jargon such as "Dude, put down the crack pipe!" or even more trendily, the text-message-y "d00d, R U Hi?"

Crack gets one high. But quaaludes cause hallucinations similar to acid...

[axn]

Hmmm.... I might have run into an interesting bug in NewPGen. When I sieved k*b^n+1 form with (b=2,n=3355583,kmin=2,kmax=16), NewPGen declared all candidates as composite, instantly. However, if i give kmin=kmax=2, NewPGen just happily keeps going without finiding any factors!!

@Jasong, Try using the sieve option "b^n+k" with b=2, nmin=nmax=3355584 and k=1. NewPGen will instantly find the factor 769.

[paulunderwood]

Originally Posted by axn1

Hmmm.... I might have run into an interesting bug in NewPGen. When I sieved k*b^n+1 form with (b=2,n=3355583,kmin=2,kmax=16), NewPGen declared all candidates as composite, instantly. However, if i give kmin=kmax=2, NewPGen just happily keeps going without finiding any factors!!

It is a bug only if you not specify "include even k":

Base = 2
Include even k's ? (y) : n
n = 3355583
kmin = 2
kmax = 2
Type : k.b^n+1
The output file newout already exists - continue? (y) : y
Are you ready to start sieving ? (y) : y
CPU capabilities: CMOV: Supported. SSE2: Supported.
Using bitmap : allocating 0.0Kb of RAM...
...succeeded
0 candidates
Sieving numbers with 1010132 decimal digits
Initialising sieve...
Done.
02:26:06 Starting sieve (reduced screen output while p < 1 billion)
Stopping...o 33554467 (33.5 million)
02:26:10 Saving results to newout...
02:26:10 ...done.
Output file 'newout' generated, contains 0 k's

Paul ought to iron this out

I have emailed him

[Jay]

Originally Posted by jasong

If you tell NewPGen to sieve k=1 to 5 for the equation k*2^3355583+1, it will say everything has been sieved and all have been found composite, and it will do that in less than a second.

Originally Posted by jasong

I'll repeat my challenge. Find a factor for 2^3355584+1 and test it without shortcuts. If my friends(or tolerators, possibly) at Riesel Sieve tell me that they've duplicated the result, then I'll shut up. Otherwise, you should seriously consider showing so-called cranks more respect.

Not certain which you want factors for, but I'll assume you mean the second.

The following factors were found via ECM using Prime95.

2^3355584+1: 769*274177*961934081

Using GMP I then obtained 2^3355584+1 Mod(f) for each factor obtained via GMP. Each resulted in a mod result of 0.

My understanding is that Prime95 uses an FFT computation in the interests of speed, while GMP uses integer math. However I could very easily be incorrect regarding these statements. However both packages are open source and nobody has ever found any errors in the computation methods of either.

Two different methods used to obtain the factors and to test the validity of factors. Both methods open source and reviewed by a large number of people.

I doubt that any conspiracy exists with the goal to ignore potential primes. It appears that 2^3355584+1 not only tests as being a composite, but also has (some) easily identifiable factors.

Was there anything else your friend would like to state, for the record?

[axn]

Originally Posted by paulunderwood

It is a bug only if you not specify "include even k":

D'oh! Of course. Still a bug, just not the one I imagined.

[jasong]

comment deleted.

[Jay]

Originally Posted by jasong

bc is running the equation ((2^3355584)+1)/789 right now.

Oops, the file gave out a number that was cut off at the top after it was printed. I want to make sure I'm doing this right, so after I solve one, I can turn around and plug in the answer in the place 789 is above. If 789 is a factor, than switching the numbers should get the result 789.

If you're attempting to triple check the factors I found, you may want to use the correct factors. I said

2^3355584+1: 769*274177*961934081