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Forum: Riesel Prime Search 2021-09-15, 07:15
Replies: 267
Views: 46,637
Posted By sweety439
https://primes.utm.edu/primes/status.php id...

https://primes.utm.edu/primes/status.php

id 132704 and 132705 are palindromes.
Forum: sweety439 2021-09-11, 03:24
Replies: 387
Views: 26,135
Posted By sweety439
Reference: Mersenne-Fermat primes...

Reference: Mersenne-Fermat primes (https://archive.ph/20120529014233/http://staff.spd.dcu.ie/johnbcos/fermat6.htm), we can also consider generalized Mersenne-Fermat primes base b, the generalized...
Forum: sweety439 2021-09-11, 03:18
Replies: 387
Views: 26,135
Posted By sweety439
List of generalized Saouter primes (i.e. primes...

List of generalized Saouter primes (i.e. primes of the form (b^(2*3^n)+b^(3^n)+1)/gcd(b-1,3)) in bases 2<=b<=1024

Compare: List of generalized Fermat primes (i.e. primes of the form...
Forum: sweety439 2021-09-10, 05:37
Replies: 177
Views: 17,131
Posted By sweety439
Newest data (minimal primes (start with b+1) up...

Newest data (minimal primes (start with b+1) up to certain limit) for bases b=17 and b=18
Forum: Aliquot Sequences 2021-09-10, 05:28
Replies: 11
Views: 752
Posted By sweety439
All strong infinity-touchable numbers are...

All strong infinity-touchable numbers are infinity-touchable, since for all nonnegative integers n, there are only finitely many positive integers m such that s(m)=n (and the largest such m is at...
Forum: Factoring 2021-09-10, 00:33
Replies: 427
Views: 73,770
Posted By sweety439
For HP(4), the smallest unsolved base is 13: ...

For HP(4), the smallest unsolved base is 13:


2,31
3,67
4,37
5,457
6,79
7,368543395659524076221303587
8,14029
Forum: Factoring 2021-09-09, 23:43
Replies: 427
Views: 73,770
Posted By sweety439
Here is the PARI/GP code, can calculate home...

Here is the PARI/GP code, can calculate home prime for all bases b>=2, just type "home(n,b)" to find the home prime for integer n in base b


step(n,b)=my(f=factor(n), v=[]); for(i=1, #f~,...
Forum: Aliquot Sequences 2021-09-09, 02:48
Replies: 11
Views: 752
Posted By sweety439
We define "strong infinity-touchable number" as...

We define "strong infinity-touchable number" as nonnegative integer n such that there exist infinitely many nonnegative integers whose Aliquot sequences reach n

e.g. all nonnegative integers <52...
Forum: Aliquot Sequences 2021-09-09, 02:47
Replies: 100
Views: 3,872
Posted By sweety439
There are amicable pairs which cannot be reached...

There are amicable pairs which cannot be reached by any aliquot sequence starting from a number that does not belong to this pair, they are listed in the OEIS sequence A238382...
Forum: sweety439 2021-09-08, 05:55
Replies: 177
Views: 17,131
Posted By sweety439
Some unsolved families are obvious through data...

Some unsolved families are obvious through data for minimal primes (start with b+1) base b up to certain limit (https://en.wikiversity.org/wiki/Quasi-minimal_prime)

Example 1: 80555551 is minimal...
Forum: sweety439 2021-09-08, 04:40
Replies: 387
Views: 26,135
Posted By sweety439
For the newest status for thread...

For the newest status for thread https://mersenneforum.org/showthread.php?t=10354
Forum: sweety439 2021-09-05, 20:35
Replies: 177
Views: 17,131
Posted By sweety439
Known unsolved families in bases b=17 and b=18: ...

Known unsolved families in bases b=17 and b=18:

b=17:


F1{9}
1{7}
15{0}D
1F{0}7
51{0}D
Forum: sweety439 2021-09-05, 20:31
Replies: 177
Views: 17,131
Posted By sweety439
Known minimal primes (start with b+1) in base...

Known minimal primes (start with b+1) in base b=18:

Small ones: (written in base b)


11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D,...
Forum: sweety439 2021-09-05, 20:27
Replies: 177
Views: 17,131
Posted By sweety439
Found by the smallest prime of the form xy{0}z or...

Found by the smallest prime of the form xy{0}z or x{0}yz which no possible prime subsequence (i.e. no possible prime of the form x{0}y, x{0}z, y{0}z): (written in base 10)


17: 11{0}1: 307
17:...
Forum: sweety439 2021-09-05, 20:23
Replies: 177
Views: 17,131
Posted By sweety439
Found by smallest generalized near-repdigit...

Found by smallest generalized near-repdigit primes (i.e. of the form x{y} or {x}y) base b: (written in base 10) (the numbers whose repeating digit (i.e. y for x{y}, or x for {x}y) is 1 are not...
Forum: sweety439 2021-09-05, 20:21
Replies: 177
Views: 17,131
Posted By sweety439
Known minimal primes (start with b+1) in base...

Known minimal primes (start with b+1) in base b=17:

Small ones: (written in base b)


12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83,...
Forum: Aliquot Sequences 2021-09-04, 14:33
Replies: 11
Views: 752
Posted By sweety439
No, there are three n such that s(n) = 284: 220,...

No, there are three n such that s(n) = 284: 220, 562, 80089=283^2, and if the stronger version of Goldbach conjecture is true, then there are infinitely many numbers whose Aliquot sequence reach the...
Forum: MattcAnderson 2021-09-04, 14:22
Replies: 6
Views: 423
Posted By sweety439
What is the natural density...

What is the natural density (https://en.wikipedia.org/wiki/Natural_density) of A056561 (https://oeis.org/A056561)? Is it zero? Or positive?
Forum: sweety439 2021-09-03, 23:36
Replies: 1,247
Views: 79,321
Posted By sweety439
Word files attached.

Word files attached.
Forum: sweety439 2021-09-03, 23:28
Replies: 1,247
Views: 79,321
Posted By sweety439
Status for 2<=b<=128 and 1<=k<=128: ...

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

Sierpinski (k*b^n+1)/gcd(k+1,b-1)...
Forum: sweety439 2021-09-03, 23:23
Replies: 1,247
Views: 79,321
Posted By sweety439
Status files: Sierpinski problems in bases...

Status files:

Sierpinski problems in bases b<=128 and b = 256, 512, 1024...
Forum: sweety439 2021-09-03, 22:48
Replies: 7
Views: 121
Posted By sweety439
sequence A128033 4,3 5,13 7,3 8,3 ...

sequence A128033


4,3
5,13
7,3
8,3
10,3
11,3
13,7
Forum: sweety439 2021-09-03, 21:18
Replies: 7
Views: 121
Posted By sweety439
sequence A125958 (a,b) = (2*n-1,-2) can be...

sequence A125958 (a,b) = (2*n-1,-2) can be extended to 2*n-1 = 231 (n = 116)


3,3
5,3
7,5
9,3
11,3
13,7
15,3
Forum: sweety439 2021-09-03, 21:12
Replies: 7
Views: 121
Posted By sweety439
Thus the primitive part of the n-th term is...

Thus the primitive part of the n-th term is Phi(n,a,b) = b^eulerphi(n) * Phi(n,(a/b))

Numbers n such that Phi(n,a,b) is prime for fixed a, b:
...
Forum: sweety439 2021-09-03, 20:47
Replies: 7
Views: 121
Posted By sweety439
sequence A125954 (a,b) = (2*n+1,2) can be...

sequence A125954 (a,b) = (2*n+1,2) can be extended to 2*n+1 = 183 (n = 91)


3,3
5,5
7,3
9,3
11,5
13,3
15,5
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