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2010-11-13, 13:35   #881
3.14159

May 2010
Prime hunting commission.

24·3·5·7 Posts

Quote:
 Originally Posted by Merfighters I think that should be 5↑5↑5↑5↑↑0.421.
5↑↑0.421 = 5↑0.421

Either way is correct.

Last fiddled with by 3.14159 on 2010-11-13 at 14:34

2010-11-13, 14:07   #882
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by 3.14159 To you, or to everyone?
Pretty much everyone, usually even including the authors of the paper introducing the new concept.

2010-11-13, 14:08   #883
CRGreathouse

Aug 2006

135418 Posts

Quote:
 Originally Posted by Merfighters I think that should be 5↑5↑5↑5↑↑0.421.
Quote:
 Originally Posted by 3.14159 5↑↑0.421 = 5↑0.421 Either way is correct.
In this case the definition is not complete!

 2010-11-13, 14:36 #884 3.14159     May 2010 Prime hunting commission. 24·3·5·7 Posts I doubt there will be any extensions to the higher operators; n↑↑↑x, n↑↑↑↑x, n↑↑↑↑↑x, n↑↑↑↑↑↑x etc.. Though there is the pentalog/pentaroot, hexalog/hexaroot, etc. 5↑↑↑1 = 5; 5↑↑↑2 = 5↑↑5 = 5↑5↑5↑5↑5 = 10↑10↑(1.3357*10↑2184). 5↑↑↑3 = 5↑↑5↑↑5 = 5↑↑(5↑5↑5↑5↑5) = 5↑↑(10↑10↑(1.3357*10↑2184)) = 5↑5↑5...↑5 (10↑10↑(1.3357*10↑2184) terms) Etc, etc. There should be a real value for 5↑↑↑2.71, or 5↑↑↑(ln(2)). For now, it remains undefined for non-integers. Last fiddled with by 3.14159 on 2010-11-13 at 15:03
 2010-11-19, 02:56 #885 3.14159     May 2010 Prime hunting commission. 168010 Posts Alright.. A prime to be submitted; 479644*10813886+1 (28242 digits) Verification: Primality testing 479644*108^13886+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using zero-padded FFT length 12K on 479644*108^13886+1 Running N-1 test using base 13 Special modular reduction using zero-padded FFT length 12K on 479644*108^13886+1 Calling Brillhart-Lehmer-Selfridge with factored part 70.38% 479644*108^13886+1 is prime! (44.5454s+0.0222s)
 2010-11-26, 21:38 #886 3.14159     May 2010 Prime hunting commission. 24×3×5×7 Posts Submissions: 254692*5412680+1 (21973 digits) 1124*2600!+1 (7760 digits) Proofs; Primality testing 254692*54^12680+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using zero-padded FFT length 10K on 254692*54^12680+1 Calling Brillhart-Lehmer-Selfridge with factored part 82.60% 254692*54^12680+1 is prime! (14.7984s+0.0015s) Primality testing 1124*2600!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2609 Generic modular reduction using generic reduction FFT length 2560 on A 25762-bit number Calling Brillhart-Lehmer-Selfridge with factored part 35.17% 1124*2600!+1 is prime! (4.3044s+0.0014s) Last fiddled with by 3.14159 on 2010-11-26 at 21:40
 2010-12-04, 17:49 #887 3.14159     May 2010 Prime hunting commission. 24·3·5·7 Posts Submissions: 7203*(700!*p(700)#)^2+1 (7879 digits). Verification: Primality testing 7203*(700!*p(700)#)^2+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5297 Generic modular reduction using generic reduction FFT length 2560 on A 26174-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.60% 7203*(700!*p(700)#)^2+1 is prime! (4.7043s+0.0013s) Last fiddled with by 3.14159 on 2010-12-04 at 17:49
 2010-12-05, 15:11 #888 lorgix     Sep 2010 Scandinavia 3·5·41 Posts 1594^1594*797#+1 (5435 digits) Primality testing 1594^1594*797#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 821 Calling Brillhart-Lehmer-Selfridge with factored part 85.16% 1594^1594*797#+1 is prime! (8.2406s+0.0142s)
2010-12-05, 16:12   #889
3.14159

May 2010
Prime hunting commission.

69016 Posts

Quote:
 Originally Posted by lorgix 1594^1594*797#+1 (5435 digits) Primality testing 1594^1594*797#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 821 Calling Brillhart-Lehmer-Selfridge with factored part 85.16% 1594^1594*797#+1 is prime! (8.2406s+0.0142s)

Entry accepted.

 2010-12-05, 18:00 #890 lorgix     Sep 2010 Scandinavia 3×5×41 Posts 4007#*4008+1 (1713 digits) Primality testing 4007#*4008+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 4051 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 4007#*4008+1 is prime! (1.9568s+0.0022s)
 2010-12-05, 20:47 #891 lorgix     Sep 2010 Scandinavia 3·5·41 Posts The following should be all primes of the form p#(p+1)+1, where p is prime and <15000 Code: Primality testing 5#*6+1 [N-1, Brillhart-Lehmer-Selfridge] small number, factored prime! 5#*6+1 is prime! (0.0578s+0.0558s) Primality testing 13#*14+1 [N-1, Brillhart-Lehmer-Selfridge] small number, factored prime! 13#*14+1 is prime! (0.0108s+0.0318s) Primality testing 17#*18+1 [N-1, Brillhart-Lehmer-Selfridge] small number, factored prime! 17#*18+1 is prime! (0.0292s+0.0459s) Primality testing 19#*20+1 [N-1, Brillhart-Lehmer-Selfridge] small number, factored prime! 19#*20+1 is prime! (0.0282s+0.0529s) Primality testing 31#*32+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Calling Brillhart-Lehmer-Selfridge with factored part 35.71% 31#*32+1 is prime! (0.3568s+0.0650s) Primality testing 1399#*1400+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 1429 Calling Brillhart-Lehmer-Selfridge with factored part 33.49% 1399#*1400+1 is prime! (0.5338s+0.0448s) Primality testing 1637#*1638+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 33.49% 1637#*1638+1 is prime! (0.4930s+0.0381s) Primality testing 2131#*2132+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2141 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 2131#*2132+1 is prime! (0.9065s+0.0165s) Primality testing 3457#*3458+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 33.53% 3457#*3458+1 is prime! (3.0264s+0.0662s) Primality testing 4007#*4008+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 4051 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 4007#*4008+1 is prime! (3.7708s+0.0573s) Primality testing 8179#*8180+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 8191 Calling Brillhart-Lehmer-Selfridge with factored part 33.39% 8179#*8180+1 is prime! (31.9143s+0.0230s) 8179#*8180+1 has 3503 digits

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