Bases 251-500 reservations/statuses/primes

[appeldorff]

I'm pretty sure i removed k=87036 from my search after you told me. I used a spreadsheet to keep score and i have 267 k's left in that spreadsheet.
But I'll take a look at the k's you list as remaining and see if I forgot to remove one.

ÊDIT: Found it. Forgot to remove k=8956 hehe.

[MyDogBuster]

An algebraic straggler.

Reserving Riesel 409.

[MyDogBuster]

Riesel Base 409
Conjectured k = 534
Covering Set = 5, 41
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 17(17)

Found Primes: 163k's File attached

Remaining k's: Tested to n=25K
144*409^n-1 < Proven composite by partial algebraic factors
284*409^n-1
344*409^n-1

Trivial Factor Eliminations: 100k's

Base Released

[MyDogBuster]

Cleaning out the closets now.

Reserving Riesel 476 & 491 and Sierp 491 to n=25K

[rogue]

I have some results to report.

Primes:

3*328^6+1
4*328^30+1
6*328^7+1
7*328^1+1
9*328^1+1
10*328^3+1
12*328^2+1
13*328^3+1
15*328^2+1
16*328^3+1
18*328^4+1
19*328^3+1
21*328^3+1
22*328^592+1
24*328^1+1
25*328^2+1
28*328^2+1
30*328^201+1
31*328^1+1
33*328^3+1
34*328^13+1
36*328^292+1
37*328^4+1
39*328^2+1
40*328^1+1
42*328^4+1
43*328^2+1
45*328^19+1
46*328^3+1

Trivially factored

2
5
8
11
14
17
20
23
26
29
32
35
38
41
44
47

I have not tested GFNs, i.e. k=1.

The only remaining k without a prime is 27. I have tested it to 25K. I am releasing this base.

[rogue]

I have some results to report.

Primes:

2*328^80-1
3*328^1-1
5*328^2-1
6*328^2-1
9*328^605-1
11*328^1-1
12*328^2-1
14*328^1-1
15*328^1-1
17*328^3-1
18*328^1-1
20*328^20962-1
21*328^3-1
23*328^2-1
24*328^4-1
26*328^1-1
27*328^2-1
29*328^1-1
30*328^1-1
32*328^22-1
33*328^2-1
35*328^6603-1
36*328^1-1
38*328^2-1
39*328^1-1
42*328^447-1
44*328^1-1
45*328^1-1
47*328^3-1

Trivially factored

1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46

The remaining k without a prime are 8 and 41. I have tested it to 25K. I am releasing this base.

[MyDogBuster]

Riesel Base 476
Conjectured k = 52
Covering Set = 3, 53
Trivial Factors k == 1 mod 5(5) and k == 1 mod 19(19)

Found Primes: 37k's File attached

Remaining k's: Tested to n=25K
49*476^n-1

Trivial Factor Eliminations: 12k's

Base Released

[MyDogBuster]

Riesel Base 491
Conjectured k = 40
Covering Set = 3, 41
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 7(7)

Found Primes: 13k's File attached

Trivial Factor Eliminations: 6k's

Conjecture Proven

[MyDogBuster]

Sierp Base 491
Conjectured k = 40
Covering Set = 3, 41
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 6 mod 7(7)

Found Primes: 13k's File attached

Trivial Factor Eliminations: 6k's

Conjecture Proven

[gd_barnes]

Reserving R257...

Proven with a highest prime of 42*257^58-1.

[mdettweiler]

To test the latest new-bases script, I decided to take a whack at a few of the lowest untested Sierpinski conjectures. Here's my results:

Sierp. base 279: conjectured k 6, proven, primes:
2*279^4+1
4*279^1+1

Sierp. base 349: conjectured k 6, proven, primes:
4*349^3+1
k=2 was eliminated by trivial factors.

Sierp. base 384: conjectured k 6, proven, primes:
2*384^1+1
3*384^1+1
4*384^21+1
5*384^2+1
k=1 is a GFN.

Sierp. base 454: conjectured k 6, proven, primes:
3*454^2+1
4*454^3+1
k=2 and k=5 eliminated by trivial factors; k=1 is a GFN.

Sierp. base 489: conjectured k 6, proven, primes:
2*489^2+1
4*489^5+1

That's all for now...don't want to inundate Gary with too many of these.