Very Prime Riesel and Sierpinski k - Page 48

Thomas11 · 2013-07-16, 08:24

Quote:

Originally Posted by robert44444uk

The candidate is still seriously powering along:

183 177684
184? 190958

Started from n=250k and already one prime:

185? 255530

robert44444uk · 2013-07-16, 13:01

Good news Thomas11 for your Sierpinski candidate and very happy to see the Riesel powering along.

This candidate has another to report with all n checked to 187965

184? 190958
185? 193804
186?? 255530

Thomas11 · 2013-07-18, 09:36

Meanwhile I completed the interval n=250-300k and found another one:

184? 190958
185? 193804
186?? 255530
187?? 294807

I will continue from n=300k.

Thomas11 · 2013-07-19, 07:47

We are getting close to 190 primes:

184? 190958
185? 193804
186?? 255530
187?? 294807
188?? 318934

robert44444uk · 2013-07-19, 08:08

Quote:

Originally Posted by Thomas11

We are getting close to 190 primes:

184? 190958
185? 193804
186?? 255530
187?? 294807
188?? 318934

My word you are going like a train! I have one more to report and also to report that 184 and 185 are correctly numbered. I am up to n=197249

184 190958
185 193804
186? 210616
187?? 255530
188?? 294807
189?? 318934 [/QUOTE]

robert44444uk · 2013-07-19, 16:02

Another found before 200K. I have completed up to 197962

186 197942
187? 210616
188? 255530
189? 294807
190? 318934

Thomas11 · 2013-07-21, 11:12

I found a nice double:

187? 210616
188? 255530
189? 294807
190? 318934
191? 334623
192? 334645

robert44444uk · 2013-07-22, 09:37

Quote:

Originally Posted by Thomas11

I found a nice double:

191? 334623
192? 334645

That's the second near miss in the stratosphere

169 111235
170 111239

I'm up to 208262 without any more primes. I'm due one I hope soon.

robert44444uk · 2013-07-24, 14:42

Oh dear, it has gone quiet around here, which means maybe we have a gap on its way.

I'm up to n=218969 with no further primes, so

187 210616 is confirmed.

Interestingly, the candidate has no twin primes to date, only 6 Sophie Germain pairs and no longer Cunningham chains.

robert44444uk · 2013-07-25, 15:25

Still no new prime, up to 219623, but with empty chunks (220000-226470) and (230000-232660) done.

I thought I would plot x=nth prime versus y=ln2(ln2(k*2^n-1)) and see what I got. As expected a very linear relationship and what's more this suggests the 200th prime at about n=475,000 unless I did the maths wrong. Actually, I think it will be greater than this value.

Thomas11 · 2013-07-25, 16:26

The plot is indeed very linear. I did similar plots for some of my Sierpinski candidates, but they are typically more "scattered".

But let me add another prime to the series:

193? 363020

The interval n=300-350k is fully tested now, continuing to 400k.

2013-07-16, 13:01	#519
robert44444uk Jun 2003 Suva, Fiji 2³×3×5×17 Posts	186!!!!! Good news Thomas11 for your Sierpinski candidate and very happy to see the Riesel powering along. This candidate has another to report with all n checked to 187965 184? 190958 185? 193804 186?? 255530

2013-07-19, 07:47	#521
Thomas11 Feb 2003 780₁₆ Posts	188!!! We are getting close to 190 primes: 184? 190958 185? 193804 186?? 255530 187?? 294807 188?? 318934

2013-07-19, 16:02	#523
robert44444uk Jun 2003 Suva, Fiji 2040₁₀ Posts	190 up! Another found before 200K. I have completed up to 197962 186 197942 187? 210616 188? 255530 189? 294807 190? 318934

2013-07-21, 11:12	#524
Thomas11 Feb 2003 11110000000₂ Posts	192!!! I found a nice double: 187? 210616 188? 255530 189? 294807 190? 318934 191? 334623 192? 334645

2013-07-25, 15:25	#527
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	Still no new prime, up to 219623, but with empty chunks (220000-226470) and (230000-232660) done. I thought I would plot x=nth prime versus y=ln2(ln2(k*2^n-1)) and see what I got. As expected a very linear relationship and what's more this suggests the 200th prime at about n=475,000 unless I did the maths wrong. Actually, I think it will be greater than this value. Attached Thumbnails

2013-07-18, 09:36	#520
Thomas11 Feb 2003 2⁷×3×5 Posts	Meanwhile I completed the interval n=250-300k and found another one: 184? 190958 185? 193804 186?? 255530 187?? 294807 I will continue from n=300k.

2013-07-24, 14:42	#526
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	Oh dear, it has gone quiet around here, which means maybe we have a gap on its way. I'm up to n=218969 with no further primes, so 187 210616 is confirmed. Interestingly, the candidate has no twin primes to date, only 6 Sophie Germain pairs and no longer Cunningham chains.

2013-07-25, 16:26	#528
Thomas11 Feb 2003 2⁷×3×5 Posts	The plot is indeed very linear. I did similar plots for some of my Sierpinski candidates, but they are typically more "scattered". But let me add another prime to the series: 193? 363020 The interval n=300-350k is fully tested now, continuing to 400k.

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