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Forum: sweety439 2020-09-28, 14:45
Replies: 1,003
Views: 32,281
Posted By sweety439
Also, there are many reservations for bases > 128...

Also, there are many reservations for bases > 128 (except 256, 512, 1024) or k's > CK:

Primes 78557<k<271129: Prime Sierpinski Problem
Composites 78557<k<271129: Extended Sierpinski Problem
S4...
Forum: sweety439 2020-09-28, 14:27
Replies: 1,003
Views: 32,281
Posted By sweety439
Reservations for the Sierpinski/Riesel problems: ...

Reservations for the Sierpinski/Riesel problems:

S2, all k except 65536: PrimeGrid's Seventeen or Bust (http://www.primegrid.com/forum_thread.php?id=1647) (status...
Forum: sweety439 2020-09-28, 14:07
Replies: 1,003
Views: 32,281
Posted By sweety439
The CK for S66 is known to be 21314443 (I have...

The CK for S66 is known to be 21314443 (I have checked it, no k<21314443 have covering set)

The CK for S120, R66, R120 are still running ....
Forum: sweety439 2020-09-28, 02:40
Replies: 1,003
Views: 32,281
Posted By sweety439
For k = 4, 64, 324, 1024, 2500, 5184, 9604,...

For k = 4, 64, 324, 1024, 2500, 5184, 9604, 16384, 26244, 40000, 58564, 82944, 114244, 153664, 202500, 262144, ... (i.e. k is of the form 4*m^4):

* All n for all 4th-power bases have algebra...
Forum: sweety439 2020-09-28, 02:16
Replies: 1,003
Views: 32,281
Posted By sweety439
Update newest file for Sierpinski problems...

Update newest file for Sierpinski problems (https://docs.google.com/document/d/e/2PACX-1vQVukcERAlTzkaLL-22PTrOWY0PHGu6EH0KApDxL4gi-8CWia-e2Wa3MKHrpj3dDCkUCYQivzG5VkVm/pub) to include the newest test...
Forum: sweety439 2020-09-28, 01:55
Replies: 1,003
Views: 32,281
Posted By sweety439
The test limit of GFN's and half GFN's: base...

The test limit of GFN's and half GFN's:

base 2:

According to http://www.prothsearch.com/fermat.html, the first numbers n>=5 such that 2^(2^n)+1 might be primes are 33, 34, 35, 40, 41, 44, 45,...
Forum: sweety439 2020-09-25, 10:27
Replies: 1,003
Views: 32,281
Posted By sweety439
Status for 2<=b<=128 and 1<=k<=128: ...

Status for 2<=b<=128 and 1<=k<=128:

Sierpinski (https://en.wikipedia.org/w/index.php?title=Wikipedia:Sandbox&oldid=980224043)

Riesel...
Forum: sweety439 2020-09-24, 07:23
Replies: 1,003
Views: 32,281
Posted By sweety439
Sierpinski conjectures and proofs...

Sierpinski conjectures and proofs (https://docs.google.com/document/d/e/2PACX-1vQPjYgjFaa0W5koDtgCNeP6y9GerLvxD1L79zfDv4U1-ah4eLG9KWg5yR5nPa3MK3F4yfMpCV9458Wi/pub)

Riesel conjectures and proofs...
Forum: sweety439 2020-09-24, 01:02
Replies: 1,003
Views: 32,281
Posted By sweety439
Conjectured smallest Sierpinski k for bases...

Conjectured smallest Sierpinski k for bases 2<=b<=2500: (NA if >5000000)


b,CK
2,78557
3,11047
4,419
5,7
6,174308
7,209
Forum: sweety439 2020-09-24, 01:01
Replies: 1,003
Views: 32,281
Posted By sweety439
Conjectured smallest Riesel k for bases...

Conjectured smallest Riesel k for bases 2<=b<=2500: (NA if >5000000)


b,CK
2,509203
3,12119
4,361
5,13
6,84687
7,457
Forum: sweety439 2020-09-24, 00:32
Replies: 1,003
Views: 32,281
Posted By sweety439
Sierpinski k=8: b = 128 has no possible prime

Sierpinski k=8: b = 128 has no possible prime
Forum: sweety439 2020-09-24, 00:32
Replies: 1,003
Views: 32,281
Posted By sweety439
proven to be composite for all n by partial...

proven to be composite for all n by partial algebraic factors:

Riesel k=1: (none)
Riesel k=2: (none)
Riesel k=3: (none)
Riesel k=4: b == 4 mod 5
Riesel k=5: (none)
Riesel k=6: b = 6*m^2 with...
Forum: sweety439 2020-09-24, 00:27
Replies: 1,003
Views: 32,281
Posted By sweety439
proven to be composite for all n (or only be...

proven to be composite for all n (or only be prime for very small n) by all algebraic factors:

Riesel k=1: b = m^r with r>1
Riesel k=2: (none)
Riesel k=3: (none)
Riesel k=4: b = m^2
Riesel...
Forum: sweety439 2020-09-23, 23:38
Replies: 1,003
Views: 32,281
Posted By sweety439
proven to be composite by covering set: ...

proven to be composite by covering set:

Riesel k=1: (none)
Riesel k=2: (none)
Riesel k=3: (none)
Riesel k=4: b == 14 mod 15
Riesel k=5: b == 11 mod 12
Riesel k=6: b == 34 mod 35
Riesel k=7:...
Forum: sweety439 2020-09-23, 23:13
Replies: 1,003
Views: 32,281
Posted By sweety439
Riesel k=9: {107, 207, 237, 325, 347, 378, 438,...

Riesel k=9: {107, 207, 237, 325, 347, 378, 438, 483, 536, 566, 570, 592, 636, 688, 705, 711, 718, 823, 830, 835, 852, 893, 907, 926, 927, 995, 1010} (totally 27 bases)
Riesel k=10: {80, 233, 262,...
Forum: sweety439 2020-09-23, 21:16
Replies: 1,003
Views: 32,281
Posted By sweety439
Riesel k=5: {31, 117, 181, 338, 411, 429, 489,...

Riesel k=5: {31, 117, 181, 338, 411, 429, 489, 499, 535, 581, 583, 631, 717, 757, 998} (totally 15 bases)
Riesel k=6: {234, 412, 549, 553, 573, 619, 750, 878, 894, 954, 986} (totally 11 bases)...
Forum: sweety439 2020-09-23, 20:02
Replies: 1,003
Views: 32,281
Posted By sweety439
See...

See https://github.com/xayahrainie4793/Sierpinski-Riesel-for-fixed-k-and-variable-base for the status of 1<=k<=12 and 2<=b<=1024, all searched to n>=6000 (n>=100000 for gcd(k+-1,b-1) (+ for...
Forum: sweety439 2020-09-23, 01:42
Replies: 11
Views: 1,588
Posted By sweety439
Problem: For given integer triple (k,b,c), k>=1,...

Problem: For given integer triple (k,b,c), k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1, find the smallest possible value for bigomega((k*b^n+c)/gcd(k+c,b-1)), where n is integer >=1
Forum: sweety439 2020-09-22, 22:56
Replies: 1,003
Views: 32,281
Posted By sweety439
Conjecture: For integer triple (k,b,c), k>=1,...

Conjecture: For integer triple (k,b,c), k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1, there is a prime of the form (k*b^n+c)/gcd(k+c,b-1) with integer n>=1 if and only if (k*b^n+c)/gcd(k+c,b-1) has no...
Forum: Cunningham Tables 2020-09-22, 22:48
Replies: 12
Views: 1,987
Posted By sweety439
10, 323- still not be started to factor (see...

10, 323- still not be started to factor (see https://homes.cerias.purdue.edu/~ssw/cun/who.txt), however, 10, 323- is the third most wanted number in...
Forum: sweety439 2020-09-22, 22:42
Replies: 1,003
Views: 32,281
Posted By sweety439
R88 have more such examples, see post...

R88 have more such examples, see post https://mersenneforum.org/showpost.php?p=196598&postcount=486
Forum: sweety439 2020-09-22, 20:52
Replies: 1,003
Views: 32,281
Posted By sweety439
Riesel case: (k*b^n-1)/gcd(k-1,b-1) Sierpinski...

Riesel case: (k*b^n-1)/gcd(k-1,b-1)
Sierpinski case: (k*b^n+1)/gcd(k+1,b-1)

If k is not rational power of b, then:

* In Riesel case, (k*b^n-1)/gcd(k-1,b-1) has algebra factors if and only if...
Forum: sweety439 2020-09-20, 22:12
Replies: 1,003
Views: 32,281
Posted By sweety439
For Riesel base b, a k-value has algebra factors...

For Riesel base b, a k-value has algebra factors if and only if there exists n such that k*b^n is perfect power

For Sierpinski base b, a k-value has algebra factors if and only if there exists n...
Forum: sweety439 2020-09-20, 22:11
Replies: 1,003
Views: 32,281
Posted By sweety439
For R40, these remain k's have algebra factors: ...

For R40, these remain k's have algebra factors:

* k=490 (=square*base/4), all odd n are algebraic
* k=11560 (=289*base, 289 itself was eliminated at n=1), all odd n are algebraic
* k=12250...
Forum: sweety439 2020-09-18, 20:38
Replies: 1,003
Views: 32,281
Posted By sweety439
k = 676: since 676 is square, all even n...

k = 676:

since 676 is square, all even n have algebra factors, and we only want to know whether it has a covering set of primes for all odd n, if so, then this k makes a full covering set with...
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