20190918, 07:31  #1 
Jun 2015
Vallejo, CA/.
2·5·97 Posts 
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 10^{999}+ 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
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 
20190919, 02:52  #2 
Jun 2015
Vallejo, CA/.
2×5×97 Posts 
TITANIC PRIMES (From count 201 to 400)
Next 200 titanic primes.
Count 201400 A074282 10^{999}+ 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
Last fiddled with by rudy235 on 20190919 at 03:47 Reason: correcting mistake 
20190919, 03:14  #3 
Jun 2003
4850_{10} Posts 
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? 
20190919, 03:57  #4 
Jun 2015
Vallejo, CA/.
2·5·97 Posts 
NEXT set of 200 titanic primes
Next 200 titanic primes.
Count 201400 A074282 10^{999}+ 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

20190919, 04:09  #5  
Jun 2015
Vallejo, CA/.
3CA_{16} Posts 
Quote:
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 10^{999}+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. 

20190919, 04:42  #6 
Jun 2003
2·5^{2}·97 Posts 
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. 
20190919, 05:43  #7 
Jun 2003
2×5^{2}×97 Posts 
It seems that the largest known in factordb is 10^999+4201621, proven in Feb 2018.

20190919, 07:18  #8 
Jun 2003
2×5^{2}×97 Posts 
List of 3507 primes between 2e6 and 1e7

20190919, 07:53  #9  
Jun 2015
Vallejo, CA/.
970_{10} Posts 
Quote:
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 10^{999}+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 (p1)/2 and (p+1)/2 for semititanic SG2 and CC2 Also I am looking to see if any 2p+1 or 2p1 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 20190919 at 08:07 Reason: answering latest axn post 

20190919, 09:38  #10 
Jun 2003
2·5^{2}·97 Posts 
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 20190919 at 09:39 
20190919, 15:40  #11 
Jun 2009
2A8_{16} Posts 
What about triplets p, p+4, p+6?

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