Quicker to prove, perhaps. Easier to find, might be debatable. That still doesn't explain why there is not a single prime of the form in the top 5k.

[QUOTE=a1call;511196]Quicker to prove, perhaps. Easier to find, might be debatable. That still doesn't explain why there is not a single prime of the form in the top 5k.[/QUOTE]

k*(2^p-1)+1 = k*2^p - (k-1). Top 5000 will list it in its normalized form.
[CODE]
579 205833*2^2976222-411665 895938 L4667 2017
580 18976*2^2976221-18975 895937 p373 2014
581 2^2976221-1 895932 G2 1997 Mersenne 36[/CODE]

Also [URL="https://primes.utm.edu/primes/page.php?id=115395"]31723 *2^1398273-507567[/URL]

Please look at the forum that linked above to see what has been done so far.

EDIT:- Hmmm...
[URL="https://primes.utm.edu/primes/page.php?id=116879"]280680 · (2^1257787 - 1) + 1[/URL]
[URL="https://primes.utm.edu/primes/page.php?id=118071"]1089904 · (2^1257787 - 1) + 1[/URL]

Not sure if the 1st one fits the bill but the last two certainly do.
You are a much better searcher than I am. My search did not turn up those.
Thank you for the reply.

Then again none of them are top 5k, are they?

[QUOTE=a1call;511201]Then again none of them are top 5k, are they?[/QUOTE]

You mean #579 & #580 are not top 5000?

Here's another one: 46821 · 2^3021380 - 374567 @ 562

I was taking about the linked items.
It's early morning here.
Thank you for the alternative listing format. I missed those earlier.

I am dabbling in finding Mersenne-Prime-based-Twin-Primes. They are generally eligible for N+/-1 deterministic tests since all the relevant prime factors would be known.
Just getting started so nothing astronomically large yet.:smile:
* Everything found using Pari=GP and PFGW
* Nothing bothered to be tested beyond being PRP's.

1.6.M3+/-1
10.6.M3+/-1
11.6.M3+/-1
21.6.M3+/-1
25.6.M3+/-1
26.6.M3+/-1
31.6.M3+/-1
34.6.M3+/-1
41.6.M3+/-1
46.6.M3+/-1
54.6.M3+/-1
55.6.M3+/-1

7.6.M5+/-1
8.6.M5+/-1
15.6.M5+/-1
22.6.M5+/-1
25.6.M5+/-1
27.6.M5+/-1
53.6.M5+/-1
60.6.M5+/-1
63.6.M5+/-1
77.6.M5+/-1

24.6.M7+/-1
30.6.M7+/-1
46.6.M7+/-1
49.6.M7+/-1
65.6.M7+/-1
101.6.M7+/-1
115.6.M7+/-1
119.6.M7+/-1
129.6.M7+/-1
149.6.M7+/-1
166.6.M7+/-1
175.6.M7+/-1
179.6.M7+/-1
231.6.M7+/-1
280.6.M7+/-1
305.6.M7+/-1
311.6.M7+/-1

367.6.M13+/-1
437.6.M13+/-1
493.6.M13+/-1
542.6.M13+/-1
592.6.M13+/-1
595.6.M13+/-1
623.6.M13+/-1
663.6.M13+/-1
672.6.M13+/-1
690.6.M13+/-1
697.6.M13+/-1

715.6.M17+/-1
833.6.M17+/-1
883.6.M17+/-1
893.6.M17+/-1
967.6.M17+/-1
970.6.M17+/-1
987.6.M17+/-1
1018.6.M17+/-1
1075.6.M17+/-1

24.6.M19+/-1
56.6.M19+/-1
101.6.M19+/-1
119.6.M19+/-1
201.6.M19+/-1
214.6.M19+/-1
311.6.M19+/-1

39.6.M31+/-1
131.6.M31+/-1
206.6.M31+/-1
290.6.M31+/-1

602.6.M61+/-1
740.6.M61+/-1

112.6.M89+/-1
265.6.M89+/-1

371.6.M107+/-1

184.6.M127+/-1

5772.6.M521+/-1

44649.6.M607+/-1
60840.6.M607+/-1
97769.6.M607+/-1
108911.6.M607+/-1
110320.6.M607+/-1
115411.6.M607+/-1
124801.6.M607+/-1

61939.6.M1279+/-1

Please feel free to add to the collection.:smile:

[B]151505.6.M2203 +/- 1 [/B]are minimal Twin-Primes for [B]M2203 [/B]with 670 dd each.:smile:

ETA:
[url]http://factordb.com/index.php?query=151505*6*%282%5E2203-1%29%2B1[/url]
[url]http://factordb.com/index.php?query=151505*6*%282%5E2203-1%29-1[/url]

[url]http://factordb.com/index.php?query=61939*6*%282%5E1279-1%29%2B1[/url]
[url]http://factordb.com/index.php?query=61939*6*%282%5E1279-1%29-1[/url]

64125.6.M2281 +/- 1 are minimal Twin-Primes for M2281 with 693 dd each.:smile:

ETA:
[url]http://factordb.com/index.php?query=64125*6*%282%5E2281-1%29%2B1[/url]
[url]http://factordb.com/index.php?query=64125*6*%282%5E2281-1%29-1[/url]

[B]533040.6.M3217 +/- 1[/B] are a pair of minimal Twin-Primes for [B]M3217[/B] with 975 dd each.:smile:
Found using Pari-GP and PFGW.

ETA:
[url]http://factordb.com/index.php?query=533040*6*%282%5E3217-1%29%2B1[/url]
[url]http://factordb.com/index.php?query=533040*6*%282%5E3217-1%29-1[/url]

[QUOTE=a1call;532318][B]533040.6.M3217 +/- 1[/B] are a pair of minimal Twin-Primes for [B]M3217[/B] with 975 dd each.:smile:
Found using Pari-GP and PFGW.
[/QUOTE]

How do you use Pari/GP in this venture?