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Forum: Wagstaff PRP Search 2021-06-29, 17:02
Replies: 16
Views: 1,286
Posted By sweety439
Only run Fermat test is dangerous, as there are...

Only run Fermat test is dangerous, as there are many Carmichael numbers, see https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests,...
Forum: Wagstaff PRP Search 2021-06-29, 16:59
Replies: 16
Views: 1,286
Posted By sweety439
Can you test all Wagstaff exponents below it?...

Can you test all Wagstaff exponents below it? Currently only the Wagstaff exponents below 10 million are tested, see https://mersenneforum.org/showthread.php?t=24185
Forum: sweety439 2021-06-29, 16:29
Replies: 154
Views: 14,212
Posted By sweety439
README for the file...

README for the file https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml:

* 12{3}45 means family {1245, 12345,...
Forum: FactorDB 2021-06-29, 08:37
Replies: 14
Views: 1,529
Posted By sweety439
I typed "B10...

I typed "B10 (http://factordb.com/index.php?query=B10)" in factordb, and the result number is still 10 instead of Bell (https://oeis.org/A000110)(10) = 115975
Forum: sweety439 2021-06-28, 09:24
Replies: 12
Views: 6,573
Posted By sweety439
this...

this (https://raw.githubusercontent.com/xayahrainie4793/text-file-stored/main/k%3E%3D2%20such%20that%20Phi(n%2Ck)%20is%20prime) is a list for all 2<=k<=4096 such that Phi(n,k) is prime. We noticed...
Forum: sweety439 2021-06-27, 13:19
Replies: 154
Views: 14,212
Posted By sweety439
We can use the sense of...

We can use the sense of http://www.iakovlev.org/zip/riesel2.pdf to conclude that the unsolved families (unsolved families are families which are neither primes (>base) found nor can be proven to...
Forum: sweety439 2021-06-27, 12:47
Replies: 1,244
Views: 75,444
Posted By sweety439
Riesel problems...

Riesel problems (https://docs.google.com/document/d/e/2PACX-1vReofbA92gRRhzqjKA3TKOqsukineM59WpM56LuRnbhB7bBFSYL6w-aTJ2IpJPWpiyCmPLOSE6gqDrR/pub) and Sierpinski problems...
Forum: Sierpinski/Riesel Base 5 2021-06-27, 09:05
Replies: 4
Views: 12,608
Posted By sweety439
Now there are: 30 Sierpinski k's remain (at...

Now there are:

30 Sierpinski k's remain (at n=3.3M): {6436, 7528, 10918, 26798, 29914, 31712, 36412, 41738, 44348, 44738, 45748, 51208, 58642, 60394, 62698, 64258, 67612, 67748, 71492, 74632,...
Forum: sweety439 2021-06-26, 13:44
Replies: 0
Views: 94
Posted By sweety439
A curious of generalized repunit primes

For given base b and given prime p:

(b^p-1)/(b-1) (http://www.fermatquotient.com/PrimSerien/GenRepu.txt) is divisible by p if and only if p divides b-1
(b^p+1)/(b+1)...
Forum: sweety439 2021-06-25, 07:29
Replies: 373
Views: 24,343
Posted By sweety439
If I only research a problem in dozenal (base...

If I only research a problem in dozenal (base 12), or if I only research a problem in bases <= 12, then I use X for ten and E for eleven, however, if I research a problem in bases including those >...
Forum: FactorDB 2021-06-25, 07:09
Replies: 14
Views: 1,529
Posted By sweety439
I want to add the first n digits for many...

I want to add the first n digits for many mathematical constants (pi, e, gamma, sqrt(2), ln(2), golden ratio, ...) in all bases 2<=b<=36, also the Smarandache numbers (https://oeis.org/A007908) and...
Forum: FactorDB 2021-06-25, 07:07
Replies: 14
Views: 1,529
Posted By sweety439
I suggest that factordb can add all these...

I suggest that factordb can add all these functions (https://mersenneforum.org/showpost.php?p=579527&postcount=12)
Forum: Math 2021-06-24, 07:56
Replies: 26
Views: 4,123
Posted By sweety439
I suggest: * Test all Wagstaff numbers with...

I suggest:

* Test all Wagstaff numbers with exponent below 15 million (at least prove or disprove that 13347311 and 13372531 are the next two Wagstaff exponents after 4031399), W13347311 and...
Forum: FactorDB 2021-06-24, 07:15
Replies: 15
Views: 8,683
Posted By sweety439
Silvester/Euclid sequence (and the sequences...

Silvester/Euclid sequence (and the sequences which I suggest in the previous post) should not stop when the number is not fully factored (e.g. n=20...
Forum: sweety439 2021-06-24, 06:57
Replies: 373
Views: 24,343
Posted By sweety439
The number of Mersenne exponents end with E...

The number of Mersenne exponents end with E should be less than that of Mersenne exponents end with 1, 5, or 7, this is because for all Sophie Germain primes p == 3 mod 4 (all such primes end with...
Forum: And now for something completely different 2021-06-24, 06:49
Replies: 47
Views: 19,434
Posted By sweety439
A new interest for "Divides Phi"

3*2^n+1 divides Phi(3*2^(n-1),2) for n = 5, 6, 8, 12, and the cofactor of them are all primes (this is the cofactor for n=12 (http://factordb.com/index.php?id=1100000000017315254)), are there any...
Forum: sweety439 2021-06-24, 02:29
Replies: 0
Views: 87
Posted By sweety439
Interesting properties about Mersenne(-related) exponents and Wagstaff(-related) exponents

Mersenne number (Mp, 2^p-1) and Wagstaff number (Wp, (2^p+1)/3):

3 (2^2-1, both Mp and Wp primes)
5 (2^2+1, both Mp and Wp primes)
7 (2^3-1 or 4^1+3, both Mp and Wp primes)
11 (a Sophie Germain...
Forum: Math 2021-06-24, 02:01
Replies: 26
Views: 4,123
Posted By sweety439
You can extended the table to include more terms...

You can extended the table to include more terms in A122834 (https://oeis.org/A122834), now this table includes all known Mersenne exponents (A000043 (https://oeis.org/A000043)) and all known...
Forum: sweety439 2021-06-24, 01:52
Replies: 154
Views: 14,212
Posted By sweety439
There are many conjectures related to this...

There are many conjectures related to this project (find all minimal primes (start with b+1) in bases 2<=b<=1024):

* Are there infinitely many Mersenne primes...
Forum: sweety439 2021-06-23, 04:57
Replies: 154
Views: 14,212
Posted By sweety439
all b^n+-2 and b^n+-(b-1) for 2<=b<=1024 tested...

all b^n+-2 and b^n+-(b-1) for 2<=b<=1024 tested to n=5000

status files attached

(z means b-1, y means b-2)

b^n+2 = (1000...0002) base b = 10002
b^n-2 = (zzz...zzzy) base b = zzzzy...
Forum: FactorDB 2021-06-23, 00:38
Replies: 15
Views: 8,683
Posted By sweety439
Silvester/Euclid sequence in factordb is...

Silvester/Euclid sequence in factordb is repeatedly x^2-x+1 until reaching a prime, I think the polynomial "x^2-x+1" can be generalized to any irreducible polynomial with positive leading coefficient...
Forum: sweety439 2021-06-22, 06:35
Replies: 1,244
Views: 75,444
Posted By sweety439
S40 completed to n=5000 344,1436 ...

S40 completed to n=5000


344,1436
1098,1910
1169,0
1229,0
1415,0
1600,0
2012,1299
Forum: sweety439 2021-06-21, 00:15
Replies: 154
Views: 14,212
Posted By sweety439
Records of length in these families for various...

Records of length in these families for various bases: (format: base (length)) (bases with "NB" or "RC" for given family are not counted)

1{0}1:

2 (2)
14 (3)
34 (5)
38 (>8388608)

1{0}2:
Forum: sweety439 2021-06-20, 04:21
Replies: 154
Views: 14,212
Posted By sweety439
Searched 1{0}2 (b^n+2) and {z}y (b^n-2) (for...

Searched 1{0}2 (b^n+2) and {z}y (b^n-2) (for bases 2<=b<=1024) up to n=5000 and found the (probable) primes 485^3164-2 and 487^3775-2

b^n+2 for all remain bases b<=711 and b^n-2 for all remain...
Forum: sweety439 2021-06-20, 03:31
Replies: 1,244
Views: 75,444
Posted By sweety439
All remain k for R40 are searched to n=5000: ...

All remain k for R40 are searched to n=5000:


157,0
490,2238
520,1329
534,0
618,0
709,0
739,0
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