Carol / Kynea Primes

[vasyannyasha]

Base 34
+1
Not 6093, but 8093
Base 42
+1
Not 2066, but 2466
Not 6424, but 8424
From my reservations.

[rogue]

While I'm busy with S3, one of my co-workers lending CPU to base 1968 found this prime: (1968^58533+1)^2-2. Unfortunately it is about 6000 digits too small to make it into the top 5000.

[vasyannyasha]

Unfortunately it is about 386 thousand digits.
6002 digits is n=911.

[VBCurtis]

Originally Posted by vasyannyasha

Unfortunately it is about 386 thousand digits.
6002 digits is n=911.

read again, sir. He didn't say it's 6000 digits. He said it's 6000 digits too small to make the top-5000 largest primes list.

[Dylan14]

For base 720, 1 <= n <= 10000, the following primes were found:

 (720^1-1)^2-2
 (720^2+1)^2-2
 (720^2-1)^2-2
 (720^91-1)^2-2
 (720^590+1)^2-2
 (720^1703-1)^2-2
 (720^7583-1)^2-2

[vasyannyasha]

My English..
Sorry, my mistake

[vasyannyasha]

Base 52 from n=1000 to 10000
No primes

Base 48 from n=1000 to 10000
Four primes

(48^1153+1)^2-2
(48^3882-1)^2-2
(48^4687+1)^2-2
(48^6123-1)^2-2

[rogue]

I have updated my page with additions and corrections.

[gd_barnes]

Base 56 is complete to n=10K. 11 primes on web page confirmed. 3 new primes found.

(56^1-1)^2-2
(56^2-1)^2-2
(56^3-1)^2-2
(56^11-1)^2-2
(56^177-1)^2-2
(56^1698-1)^2-2

(56^8+1)^2-2
(56^14+1)^2-2
(56^73+1)^2-2
(56^122+1)^2-2
(56^136+1)^2-2
(56^706+1)^2-2
(56^5411+1)^2-2
(56^7771+1)^2-2

Base 58 is complete to n=10K. 6 primes on web page confirmed. 3 new primes found.

(58^88-1)^2-2
(58^1720-1)^2-2

(58^2+1)^2-2
(58^21+1)^2-2
(58^35+1)^2-2
(58^213+1)^2-2
(58^296+1)^2-2
(58^1734+1)^2-2
(58^2354+1)^2-2

[gd_barnes]

Base 202 is complete to n=10K. 11 new primes found.

(202^63-1)^2-2

(202^3+1)^2-2
(202^5+1)^2-2
(202^17+1)^2-2
(202^68+1)^2-2
(202^580+1)^2-2
(202^858+1)^2-2
(202^1100+1)^2-2
(202^2323+1)^2-2
(202^3893+1)^2-2
(202^4942+1)^2-2

[gd_barnes]

I have run a doublecheck to n=2500 for all bases shown in this link: http://www.mersenneforum.org/rogue/ckps.html plus base 202 recently searched by me plus bases 1656, 2482, and 2634 previously searched by Sergey.

30 errors were found as follows:

missing primes to add:
(24^92-1)^2-2
(62^212+1)^2-2
(62^761+1)^2-2
(76^1+1)^2-2
(76^2+1)^2-2
(86^1120-1)^2-2
(86^2053-1)^2-2
(88^5-1)^2-2
(88^9-1)^2-2
(90^676+1)^2-2
(156^1663-1)^2-2
(204^2-1)^2-2
(204^1+1)^2-2
(252^1+1)^2-2

composites to remove:
(76^85-1)^2-2 has factor 13799
(78^2+1)^2-2 has factor 41
(86^5-1)^2-2 has factor 7
(86^9-1)^2-2 has factor 71
(88^1120-1)^2-2 has factor 7
(88^2053-1)^2-2 has factor 7
(154^1495+1)^2-2 has factor 89

incorrect primes to change:
(66^956+1)^2-2 has factor 7; should be (66^945+1)^2-2
(78^1+1)^2-2 has factor 17; should be (78^1-1)^2-2 [change from +1 to -1 side]
(92^1785+1)^2-2 has factor 17; should be (92^1795+1)^2-2
(142^1+1)^2-2 has factor 7; should be (142^3+1)^2-2
(170^43+1)^2-2 has factor 7; should be (170^53+1)^2-2
(186^493+1)^2-2 has factor 311; should be (186^459+1)^2-2
(204^7-1)^2-2 has factor 31; should be (204^7+1)^2-2 [change from -1 to +1 side]
(214^1572-1)^2-2 has factor 38303; should be (214^1571-1)^2-2
(252^330-1)^2-2 has factor 34720896673; should be (252^1330-1)^2-2

3 cosmetic errors were also found:

(2^17+1)^2-2; There is no space between commas; i.e. 17,18.
(18^10208-1)^2-2 There are two commas after.
(28^5048+1)^2-2 There is no comma after.

Analysis: Small primes (n<10) and commas seem to be an issue.

To help with the corrections, I have attached all primes found for n<=2500 in the order that you can easily update them on the pages. The first file is for bases <= 204 and the second one is for bases > 204.