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Forum: sweety439 2020-09-25, 10:27
Replies: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 1,564
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: 997
Views: 31,991
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: 1,915
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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: 997
Views: 31,991
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...
Forum: sweety439 2020-09-18, 19:14
Replies: 997
Views: 31,991
Posted By sweety439
For the case for R106: k = 64: since 64...

For the case for R106:

k = 64:

since 64 is square and cube, all even n and all n divisible by 3 have algebra factors, and we only want to know whether it has a covering set of primes for all n...
Forum: sweety439 2020-09-18, 18:58
Replies: 997
Views: 31,991
Posted By sweety439
We consider (289*40^n-1)/3 (which is prime for...

We consider (289*40^n-1)/3 (which is prime for n=1, but there may be covering set for n>1 (and the prime for n=1 (i.e. 3853) must be in the covering set), we should check it: (k=289 for odd n):
...
Forum: sweety439 2020-09-17, 19:28
Replies: 997
Views: 31,991
Posted By sweety439
The case for R40 k=490, since all odd n have...

The case for R40 k=490, since all odd n have algebra factors, we only consider even n:

n-value : factors
2 : 3^3 · 9679
4 : 43 · 79 · 83 · 1483
6 : 881 · 759379493
8 : 3 · 356807111111111
10...
Forum: Lounge 2020-09-17, 18:10
Replies: 1,494
RIP
Views: 97,827
Posted By sweety439
Alien Huang...

Alien Huang (https://en.wikipedia.org/wiki/Alien_Huang), age 36

an actor and television host
Forum: Conjectures 'R Us 2020-09-17, 17:12
Replies: 30
Views: 1,806
Posted By sweety439
Also, 31^5-55758 is prime, thus the mixed Riesel...

Also, 31^5-55758 is prime, thus the mixed Riesel conjecture base 31 is also a theorem.

For the S37 case, 37^1+94, 37^5+1272, and 37^2+2224 are primes, thus the mixed Sierpinski conjecture base 37...
Forum: Conjectures 'R Us 2020-09-17, 16:55
Replies: 30
Views: 1,806
Posted By sweety439
The mixed Sierpinski/Riesel conjectures for prime bases

This project is from the article http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf, this article is about the mixed Sierpinski (base 2) theorem, which is that for every odd...
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