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Old 2019-09-18, 07:31   #1
rudy235
 
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Default The First Titanic Primes

As everyone here knows the definition of a Titanic Prime (as by Sam Yates) is a prime with at least 1000 digits. And by first we now mean smallest possible, not earliest discovery.

First 200 titanic primes. A074282
10999+
Code:
7
663
2,121
2,593
3,561
4,717
5,863
9,459
11,239
14,397
17,289
18,919
19,411
21,667
25,561
26,739
27,759
28,047
28,437
28,989
35,031
41,037
41,409
41,451
43,047
43,269
43,383
50,407
51,043
52,507
55,587
59,877
61,971
62,919
63,177
69,229
70,777
71,893
73,203
73,209
75,301
76,447
76,969
78,463
79,923
82,243
85,837
85,971
90,079
91,737
94,281
94,699
96,081
97,807
102,133
104,461
105,219
121,503
122,163
122,833
122,901
124,381
126,691
129,303
130,513
133,767
136,803
137,821
137,997
140,769
143,751
144,771
145,689
145,879
146,293
151,303
152,781
153,943
155,887
155,911
156,589
158,199
163,959
164,719
165,783
168,333
170,889
171,741
175,203
176,311
177,019
184,069
184,623
184,993
187,021
189,829
195,333
197,629
198,379
201,009
203,959
207,801
209,559
211,941
212,769
213,763
216,421
217,507
218,229
220,671
221,067
224,223
228,109
228,331
232,041
233,161
237,853
247,797
250,773
252,679
252,753
254,139
254,973
255,213
259,159
259,219
262,129
263,449
265,983
271,047
273,349
279,129
280,221
286,993
286,999
288,609
290,077
291,493
294,177
294,199
296,449
299,931
303,679
306,903
307,599
310,083
310,491
311,833
312,153
314,209
317,497
318.789
322,377
322,837
323,673
324,111
325,773
326,251
326,659
329,313
330,451
331,897
332,419
334,801
335,253
335,859
336,231
336,297
336,639
337,801
340,689
343,017
348,277
348,957
363,723
366,181
373,981
376,929
380,203
380,263
381,147
382,261
383,743
384,621
385,809
389,419
391,671
393,189
402,807
403,207
404,311
406,903
407,781
408,361
410,907
412,227
412,473
414,577
417,303
418,357
Things worth mentioning within the first 200 primes.
  1. First Titanic Prime 10999+7
  2. First Sexy prime pair. After number 73203
  3. Largest Gap 16284. After number 105219 Merit= 7.08
  4. GAP of 2310 Primorial 7. After number 126691
  5. 2nd Sexy prime pair. After number 286993
  6. AP3 61971 (1) d=29766
  7. AP3 91737 (2)
  8. AP3 121503 (3)

Chris Caldwell's page lists only 55 titanic primes of exactly 1000 digits.

The first 101 Titanic Primes were proven by Jens Kruse Andersen in 2005
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Old 2019-09-19, 02:52   #2
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Default TITANIC PRIMES (From count 201 to 400)

Next 200 titanic primes.
Count 201-400 A074282
10999+

Code:
418,863
421,173
425,343
426,573
427,413
427,581
428,899
432,579
433,167
435,643
436,917
439,917
442,101
442,941
447,939
448,431
449,017
452,179
455,199
458,523
459,051
461,299
461,421
461,793
463,083
467,613
468,451
470,607
471,573
473,083
473,197
479,721
480,067
480,141
481,683
482,419
490,401
490,653
493,183
495,259
496,023
496,621
497,683
499,317
503,241
505,189
506,197
506,467
507,091
507,999
508,029
512,629
514,897
516,631
519,363
520,113
520,159
526,603
526,663
527,823
529,963
536,389
536,659
541,149
541,453
543,987
547,137
550,407
554,817
559,579
567,559
569,287
571,081
571,213
572,101
576,721
580,741
582,151
583,893
588,793
593,577
594,499
598,593
601,419
610,323
612,871
617,407
620,721
622,969
623,367
624,057
624,909
626,481
631,617
631,707
632,001
635,281
635,773
637,569
647,733
648,577
650,401
655,521
662,973
676,429
677,079
677,407
679,711
682,393
683,097
683,917
685,687
688,707
689,799
690,349
693,313
693,819
694,969
698,269
700,711
701,833
702,063
703,629
703,731
703,831
704,073
708,381
712,081
713,097
713,143
716,799
721,123
721,873
724,183
724,743
729,229
729,963
731,847
732,207
733,189
738,111
741,813
743,479
745,531
751,749
752,163
753,447
758,289
758,427
761,329
765,847
766,863
769,257
778,269
782,361
782,661
788,571
789,051
790,083
790,281
795,403
795,729
796,813
806,461
809,701
810,049
811,729
812,719
813,409
815,919
743,479
745,531
751,749
752,163
753,447
758,289
758,427
761,329
765,847
766,863
769,257
778,269
782,361
782,661
788,571
789,051
790,083
790,281
795,403
795,729
796,813
806,461
809,701
810,049
811,729
812,719
813,409
815,919
818,617
Things to mention on the second set of 200 titanic primes
  1. 10999 +507999 p First Gap of 30 (5#)
  2. 10999 +508029 p+30
  3. 10999 +418863 p Second Gap of 2310 (7#)
  4. 10999 +421173 p+2310
  5. 10999 +507999 p First Gap of 30 (5#)
  6. 10999+508029 p+30
  7. 10999+547137 Semi-Titanic Cunningham Chain (2p-1)

Last fiddled with by rudy235 on 2019-09-19 at 03:47 Reason: correcting mistake
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Old 2019-09-19, 03:14   #3
axn
 
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How are you generating these primes?
Are you proving them primes or just PRP test?
How much further are you planning to take this? Why?
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Old 2019-09-19, 03:57   #4
rudy235
 
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Default NEXT set of 200 titanic primes

Next 200 titanic primes.
Count 201-400 A074282
10999+

Code:
418,863
421,173
425,343
426,573
427,413
427,581
428,899
432,579
433,167
435,643
436,917
439,917
442,101
442,941
447,939
448,431
449,017
452,179
455,199
458,523
459,051
461,299
461,421
461,793
463,083
467,613
468,451
470,607
471,573
473,083
473,197
479,721
480,067
480,141
481,683
482,419
490,401
490,653
493,183
495,259
496,023
496,621
497,683
499,317
503,241
505,189
506,197
506,467
507,091
507,999
508,029
512,629
514,897
516,631
519,363
520,113
520,159
526,603
526,663
527,823
529,963
536,389
536,659
541,149
541,453
543,987
547,137
550,407
554,817
559,579
567,559
569,287
571,081
571,213
572,101
576,721
580,741
582,151
583,893
588,793
593,577
594,499
598,593
601,419
610,323
612,871
617,407
620,721
622,969
623,367
624,057
624,909
626,481
631,617
631,707
632,001
635,281
635,773
637,569
647,733
648,577
650,401
655,521
662,973
676,429
677,079
677,407
679,711
682,393
683,097
683,917
685,687
688,707
689,799
690,349
693,313
693,819
694,969
698,269
700,711
701,833
702,063
703,629
703,731
703,831
704,073
708,381
712,081
713,097
713,143
716,799
721,123
721,873
724,183
724,743
729,229
729,963
731,847
732,207
733,189
738,111
741,813
743,479
745,531
751,749
752,163
753,447
758,289
758,427
761,329
765,847
766,863
769,257
778,269
782,361
782,661
788,571
789,051
790,083
790,281
795,403
795,729
796,813
806,461
809,701
810,049
811,729
812,719
813,409
815,919
818,617
820,693
827,613
829,597
830,091
830,407
833,397
833,511
833,991
834,651
838,119
838,359
839,331
844,441
844,777
845,163
847,279
847,503
850,693
854,301
855,733
857,199
857,619
860,827
862,999
863,037
868,273
869,893
871,731
Things to mention on the second set of 200 titanic primes
  1. 10999 +507999 p First Gap of 30 (5#)
  2. 10999 +508029 p+30
  3. 10999 +418863 p Second Gap of 2310 (7#)
  4. 10999 +421173 p+2310
  5. 10999 +507999 p First Gap of 30 (5#)
  6. 10999+508029 p+30
  7. 10999+547137 Semi-Titanic Cunningham Chain (2p-1)
  8. 10999 +721873 p Second Gap of 2310 (7#)
  9. 10999 +724184 p+2310
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Old 2019-09-19, 04:09   #5
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Quote:
Originally Posted by axn View Post
How are you generating these primes?
Are you proving them primes or just PRP test?
How much further are you planning to take this? Why?
I am using a strong pseudoprime test BPSW
I am only proving 10% of randomly selected results and up to now all tested have come as prime.
I don't really know for sure but if I want to prove 10% random results I suppose I should be able to do 5000 in total or up 10999+10^7
I am also proving them if they come out as a TWIN, Sexy, SG primes and CC primes
Why? Well because the bottleneck is proving deterministically.
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Old 2019-09-19, 04:42   #6
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Here are the first 872 primes < 10^999 + 2e6. Spot checking in factordb, it seems all of them are known (and proven) in factordb circa Jan/Feb 2017.

Your list is missing 567879 and 577317, btw.
Attached Files
File Type: txt titanic.txt (7.2 KB, 30 views)
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Old 2019-09-19, 05:43   #7
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It seems that the largest known in factordb is 10^999+4201621, proven in Feb 2018.
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Old 2019-09-19, 07:18   #8
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List of 3507 primes between 2e6 and 1e7
Attached Files
File Type: txt titanic2.txt (30.8 KB, 31 views)
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Old 2019-09-19, 07:53   #9
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Quote:
Originally Posted by axn View Post
Here are the first 872 primes < 10^999 + 2e6. Spot checking in factordb, it seems all of them are known (and proven) in factordb circa Jan/Feb 2017.

Your list is missing 567879 and 577317, btw.
Ok First things first!
Thank you very much for posting the list of the first (872 proven?) Primes. It is a great help.

My Googling abilities are not what they used to be as I was not able to find any information when I imputed some of the PRPs I was finding.

The good news is that both 567879 and 577317 were on my original lists. I guess I did more manipulation than needed when I transcribed the info into the forum. Too much jet lag and too much Pinot Grigio is my excuse and I'm sticking with it .

I have actually PRP'ed 1000 primes the last one #1000 is 10999+2297223

All the 872 primes on the list you published are in my list (but only as PRPs). I have only managed to prove about 10% of the first 400. The rest (from 401 to 1000) are only as PRPs except for a handful of "special" cases.

But I am also looking for other things and not just listing the primes.
I am testing for gaps of 2, 4, 6, 30, 210 and 2310 [4 and primorials]
I am checking for AP3, AP4, Triplets (p, p+2, p+6)
I am also trying to find a GAP of at least 10.0 Merit. Good luck with that! I don't believe I will find ever find one.
I am checking every PRP in the list for (p-1)/2 and (p+1)/2 for semi-titanic SG2 and CC2
Also I am looking to see if any 2p+1 or 2p-1 is a prime.
So far there are some results but I will put them once I verify that at least this very few findings are indeed Primes.

So far no Gap of 4 or of 210
Yes to 1 SG pair
Yes to 1 CC of 2
Yes to an AP4 with d=79890

Also, I will put a txt file of the last 128 PRP –from #873 to #1000– once I am able to satisfy myself that at least 10% are primes.

Edit: ok the titanics for your list also match those I have up to 2297223. I guess I should only try to process the info and see if I can find the first Triplet hiding somewhere in there. LOL

Last fiddled with by rudy235 on 2019-09-19 at 08:07 Reason: answering latest axn post
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Old 2019-09-19, 09:38   #10
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Yes, all the primes up to 10^999+4201621 is proven using ECPP (not by me) and available at factordb.com.

EDIT:- The rest are all PRP (BPSW - Pari/GP).

Last fiddled with by axn on 2019-09-19 at 09:39
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Old 2019-09-19, 15:40   #11
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What about triplets p, p+4, p+6?
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