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 2017-11-30, 10:52 #122 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 22·3·5 Posts Some typos Base 34 +1 Not 6093, but 8093 Base 42 +1 Not 2066, but 2466 Not 6424, but 8424 From my reservations.
 2017-11-30, 19:40 #123 rogue     "Mark" Apr 2003 Between here and the 570310 Posts 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.
 2017-11-30, 20:30 #124 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 748 Posts Unfortunately it is about 386 thousand digits. 6002 digits is n=911.
2017-11-30, 21:11   #125
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

10000010101112 Posts

Quote:
 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.

 2017-12-01, 02:50 #126 Dylan14     "Dylan" Mar 2017 46810 Posts For base 720, 1 <= n <= 10000, the following primes were found: Code:  (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
 2017-12-01, 07:02 #127 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 22·3·5 Posts My English.. Sorry, my mistake
 2017-12-03, 19:02 #128 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 22×3×5 Posts base 48 and 52 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
 2017-12-28, 18:00 #129 rogue     "Mark" Apr 2003 Between here and the 3×1,901 Posts I have updated my page with additions and corrections.
 2018-01-12, 22:39 #130 gd_barnes     May 2007 Kansas; USA 13·19·41 Posts 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
 2018-01-14, 10:06 #131 gd_barnes     May 2007 Kansas; USA 13·19·41 Posts 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
2018-01-14, 11:43   #132
gd_barnes

May 2007
Kansas; USA

13·19·41 Posts
doublecheck to n=2500; errors

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:

(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.
Attached Files
 prime-near-squares-base2-204-2.5K.txt (12.5 KB, 18 views) prime-near-squares-base-gt204-2.5K.txt (1.2 KB, 23 views)

Last fiddled with by gd_barnes on 2018-01-14 at 12:00

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