Thread for posting tiny primes - Page 43

CRGreathouse · 2010-09-10, 12:49

Quote:

Originally Posted by 3.14159

As if what you give is any more correct.

Yes, actually. The value is known unconditionally to fall in the range

4.34918365 * 10⁹⁹⁵ to
4.34918393 * 10⁹⁹⁵.

which specifically excludes your estimate. Under the Riemann Hypothesis, the value is

Code:

4.349183651345391174173494401909821175858835012787749165345668159640929917692017520508025158032672749140951055115782715284329642530237156087125124810263387278508968321658911766258523465886512725977808272634984452430455600066331068026911186986701004309020493441689500534188494303684135964291048326520775148989368729408560690565077811567161853319863692842811424426341225271155850381084777091151663905726140220696441497991610961274270332992598688661934080913700499136923763822695771503812449781520... * 10⁹⁹⁵

where the next decimal place is almost surely 6 (but this is not known).

3.14159 · 2010-09-10, 14:56

Submissions:

For item 1. 13945 * 2¹⁴⁸⁷⁰ + 1 (4481 digits)

Verification:
Primality testing 13945*2^14870+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using all-complex FFT length 1024 on 13945*2^14870+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.91%
13945*2^14870+1 is prime! (0.1941s+0.0007s)

For item 2. 14260 * 18⁶⁸⁷⁰ + 1 (8628 digits)

Verification:
Primality testing 14260*18^6870+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Special modular reduction using zero-padded FFT length 3072 on 14260*18^6870+1
Calling Brillhart-Lehmer-Selfridge with factored part 75.98%
14260*18^6870+1 is prime! (1.4899s+0.0011s)

3.14159 · 2010-09-10, 15:37

Strangely, I can't remember my old record of 8608 digits.. I know I used b = 2 for it, and I think the k value was 28583. (I found this sometime in May or June.)

No such value appeared.. 28583 must have been the exponent.

I used to have it in my old prime collection file, which was wiped away along with the 100 GB I lost.

CRGreathouse · 2010-09-10, 16:23

Probably 1091 * 2^28583 + 1.

3.14159 · 2010-09-10, 16:42

Well, there is 1091, 7799, etc..

Wait.. come to think of it.. I think it might have been 1091.

CRGreathouse · 2010-09-10, 17:56

Quote:

Originally Posted by 3.14159

Well, there is 1091, 7799, etc..

7799 * 2^28583 + 1 has 8609 digits, so that wasn't your number. There aren't any 8608-digit numbers of the form k * 2^28583 - 1, either.

3.14159 · 2010-09-10, 20:28

So, 1091 it is.

Also: Sieving for k * 1999¹⁰⁴⁸⁰ + 1.

Base 1999 has given primes somewhat quickly on the occasions that I happened to search for it.

The exponents that I have found a prime for are 5040, 8560, and 5346. All happened quickly.

3.14159 · 2010-09-10, 20:29

However, the factorial and primorial bases give primes the fastest.

The current record for item 3 stands at 2093 * 600!²⁶ + 1, at 36614 digits.

3.14159 · 2010-09-11, 19:07

Submission: 41650 * 14¹⁷⁹⁰⁰ + 1 (20521 digits)

Verification:

Primality testing 41650*14^17900+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using all-complex FFT length 6K on 41650*14^17900+1
Calling Brillhart-Lehmer-Selfridge with factored part 73.73%
41650*14^17900+1 is prime! (9.5173s+0.0014s)

Gained another entry for item 2.

3.14159 · 2010-09-12, 01:06

Not to mention, it is also in the subset of primes with a prime number of digits.

3.14159 · 2010-09-12, 17:39

Submissions: 455679 * 2⁸⁹⁴⁹⁰ + 1 (26945 digits)

Verification:

Primality testing 455679*2^89490+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using zero-padded FFT length 10K on 455679*2^89490+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
455679*2^89490+1 is prime! (16.8968s+0.0011s)

2010-09-10, 14:56	#464
3.14159 May 2010 Prime hunting commission. 690₁₆ Posts	Submissions: For item 1. 13945 * 2¹⁴⁸⁷⁰ + 1 (4481 digits) Verification: Primality testing 139452^14870+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Special modular reduction using all-complex FFT length 1024 on 139452^14870+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.91% 139452^14870+1 is prime! (0.1941s+0.0007s) For item 2. 14260 18⁶⁸⁷⁰ + 1 (8628 digits) Verification: Primality testing 1426018^6870+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Special modular reduction using zero-padded FFT length 3072 on 1426018^6870+1 Calling Brillhart-Lehmer-Selfridge with factored part 75.98% 1426018^6870+1 is prime! (1.4899s+0.0011s) Last fiddled with by 3.14159 on 2010-09-10 at 15:32*

2010-09-10, 15:37	#465
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Strangely, I can't remember my old record of 8608 digits.. I know I used b = 2 for it, and I think the k value was 28583. (I found this sometime in May or June.) No such value appeared.. 28583 must have been the exponent. I used to have it in my old prime collection file, which was wiped away along with the 100 GB I lost. Last fiddled with by 3.14159 on 2010-09-10 at 15:43

2010-09-10, 16:42	#467
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Well, there is 1091, 7799, etc.. Wait.. come to think of it.. I think it might have been 1091. Last fiddled with by 3.14159 on 2010-09-10 at 16:47

2010-09-10, 20:28	#469
3.14159 May 2010 Prime hunting commission. 11010010000₂ Posts	So, 1091 it is. Also: Sieving for k * 1999¹⁰⁴⁸⁰ + 1. Base 1999 has given primes somewhat quickly on the occasions that I happened to search for it. The exponents that I have found a prime for are 5040, 8560, and 5346. All happened quickly. Last fiddled with by 3.14159 on 2010-09-10 at 20:31

2010-09-10, 20:29	#470
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	However, the factorial and primorial bases give primes the fastest. The current record for item 3 stands at 2093 * 600!²⁶ + 1, at 36614 digits. Last fiddled with by 3.14159 on 2010-09-10 at 20:30

2010-09-10, 16:23	#466
CRGreathouse Aug 2006 3·1,993 Posts	Probably 1091 * 2^28583 + 1.

2010-09-11, 19:07	#471
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Submission: 41650 * 14¹⁷⁹⁰⁰ + 1 (20521 digits) Verification: Primality testing 4165014^17900+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Special modular reduction using all-complex FFT length 6K on 4165014^17900+1 Calling Brillhart-Lehmer-Selfridge with factored part 73.73% 4165014^17900+1 is prime! (9.5173s+0.0014s) Gained another entry for item 2. Last fiddled with by 3.14159 on 2010-09-11 at 19:14*

2010-09-12, 01:06	#472
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Not to mention, it is also in the subset of primes with a prime number of digits.

2010-09-12, 17:39	#473
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Submissions: 455679 * 2⁸⁹⁴⁹⁰ + 1 (26945 digits) Verification: Primality testing 4556792^89490+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using zero-padded FFT length 10K on 4556792^89490+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 4556792^89490+1 is prime! (16.8968s+0.0011s) Last fiddled with by 3.14159 on 2010-09-12 at 17:40*

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