20101113, 13:35  #881 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
5↑↑0.421 = 5↑0.421
Either way is correct. Last fiddled with by 3.14159 on 20101113 at 14:34 
20101113, 14:07  #882 
Aug 2006
3^{2}×5×7×19 Posts 

20101113, 14:08  #883 
Aug 2006
13541_{8} Posts 

20101113, 14:36  #884 
May 2010
Prime hunting commission.
2^{4}·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 nonintegers. Last fiddled with by 3.14159 on 20101113 at 15:03 
20101119, 02:56  #885 
May 2010
Prime hunting commission.
1680_{10} Posts 
Alright.. A prime to be submitted;
479644*108^{13886}+1 (28242 digits) Verification: Primality testing 479644*108^13886+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Special modular reduction using zeropadded FFT length 12K on 479644*108^13886+1 Running N1 test using base 13 Special modular reduction using zeropadded FFT length 12K on 479644*108^13886+1 Calling BrillhartLehmerSelfridge with factored part 70.38% 479644*108^13886+1 is prime! (44.5454s+0.0222s) 
20101126, 21:38  #886 
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
Submissions: 254692*54^{12680}+1 (21973 digits)
1124*2600!+1 (7760 digits) Proofs; Primality testing 254692*54^12680+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Special modular reduction using zeropadded FFT length 10K on 254692*54^12680+1 Calling BrillhartLehmerSelfridge with factored part 82.60% 254692*54^12680+1 is prime! (14.7984s+0.0015s) Primality testing 1124*2600!+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2609 Generic modular reduction using generic reduction FFT length 2560 on A 25762bit number Calling BrillhartLehmerSelfridge with factored part 35.17% 1124*2600!+1 is prime! (4.3044s+0.0014s) Last fiddled with by 3.14159 on 20101126 at 21:40 
20101204, 17:49  #887 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
Submissions: 7203*(700!*p(700)#)^2+1 (7879 digits).
Verification: Primality testing 7203*(700!*p(700)#)^2+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5297 Generic modular reduction using generic reduction FFT length 2560 on A 26174bit number Calling BrillhartLehmerSelfridge with factored part 33.60% 7203*(700!*p(700)#)^2+1 is prime! (4.7043s+0.0013s) Last fiddled with by 3.14159 on 20101204 at 17:49 
20101205, 15:11  #888 
Sep 2010
Scandinavia
3·5·41 Posts 
1594^1594*797#+1 (5435 digits)
Primality testing 1594^1594*797#+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 821 Calling BrillhartLehmerSelfridge with factored part 85.16% 1594^1594*797#+1 is prime! (8.2406s+0.0142s) 
20101205, 16:12  #889 
May 2010
Prime hunting commission.
690_{16} Posts 

20101205, 18:00  #890 
Sep 2010
Scandinavia
3×5×41 Posts 
4007#*4008+1 (1713 digits)
Primality testing 4007#*4008+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 4051 Calling BrillhartLehmerSelfridge with factored part 33.36% 4007#*4008+1 is prime! (1.9568s+0.0022s) 
20101205, 20:47  #891 
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 [N1, BrillhartLehmerSelfridge] small number, factored prime! 5#*6+1 is prime! (0.0578s+0.0558s) Primality testing 13#*14+1 [N1, BrillhartLehmerSelfridge] small number, factored prime! 13#*14+1 is prime! (0.0108s+0.0318s) Primality testing 17#*18+1 [N1, BrillhartLehmerSelfridge] small number, factored prime! 17#*18+1 is prime! (0.0292s+0.0459s) Primality testing 19#*20+1 [N1, BrillhartLehmerSelfridge] small number, factored prime! 19#*20+1 is prime! (0.0282s+0.0529s) Primality testing 31#*32+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 37 Calling BrillhartLehmerSelfridge with factored part 35.71% 31#*32+1 is prime! (0.3568s+0.0650s) Primality testing 1399#*1400+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 1429 Calling BrillhartLehmerSelfridge with factored part 33.49% 1399#*1400+1 is prime! (0.5338s+0.0448s) Primality testing 1637#*1638+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2 Calling BrillhartLehmerSelfridge with factored part 33.49% 1637#*1638+1 is prime! (0.4930s+0.0381s) Primality testing 2131#*2132+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2141 Calling BrillhartLehmerSelfridge with factored part 33.36% 2131#*2132+1 is prime! (0.9065s+0.0165s) Primality testing 3457#*3458+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2 Calling BrillhartLehmerSelfridge with factored part 33.53% 3457#*3458+1 is prime! (3.0264s+0.0662s) Primality testing 4007#*4008+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 4051 Calling BrillhartLehmerSelfridge with factored part 33.36% 4007#*4008+1 is prime! (3.7708s+0.0573s) Primality testing 8179#*8180+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 8191 Calling BrillhartLehmerSelfridge with factored part 33.39% 8179#*8180+1 is prime! (31.9143s+0.0230s) 
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