20150123, 17:40  #12 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,497 Posts 
Skipping a few intermediate records, here is one that could be a decent candidate for someone with the next version of Primo:
10^310472*10^268021 is prime and 10^310472*10^268023 is a Fermat and Lucas PRP! (That's a 99...99799...999 and 99...99799...997 nearrepdigit twin pair.) 
20150214, 16:19  #13  
"Sastry Karra"
Jul 2009
Bridgewater, NJ (USA)
3^{3} Posts 
Quote:


20150222, 17:40  #14 
Sep 2002
Database er0rr
2×3^{2}×11×19 Posts 
10^468772*10^125681 is just one example of the many NRDs recently submitted to Henri's PRP database by Serge Batalov, which is provable with N+1 factored over 25%. Why have you not proved these, Serge?
Last fiddled with by paulunderwood on 20150222 at 17:46 
20150222, 18:37  #15 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,497 Posts 
Because there was a ton of them, and even more with >29% (which I didn't submit). The comment there says it all (they are a dataset for anyone who wants to learn CHG in practice).
The real search target were twins. (and the sieve was for twins, so whatever was found is far from a complete list primes/PRPs) Kamada has a systematic (x,y) pair list up to a certain limit. 
20150228, 09:24  #16  
Sep 2002
Database er0rr
111010110010_{2} Posts 
Quote:
Factoring N1: Code:
./pfgw64 o f1000 q"(10^468772*10^125682)/(2*3*6449*138176897)" PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Factoring numbers to 1000% of normal. (10^468772*10^125682)/(2*3*6449*138176897) has no small factor. Code:
./pfgw64 o f1000 q"5*10^343081" PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Factoring numbers to 1000% of normal. 5*10^343081 has no small factor. Code:
2 3 6449 138176897 2 10^12568 Code:
./pfgw64 tc hchg_helper.6 q"10^468772*10^125681" PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 10^468772*10^125681 [N1/N+1, BrillhartLehmerSelfridge] Reading factors from helper file chg_helper.6 Running N1 test using base 3 Running N+1 test using discriminant 17, base 1+sqrt(17) 10^468772*10^125681 is Fermat and Lucas PRP! (265.8579s+0.0002s) Code:
n=10^468772*10^125681; F=2*3*6449*138176897; G=2*10^12568; Code:
allocatemem(128*1024*1024); \\ Increase stack to 64mb for now \\ You may have to bump this up to 128M for really \\ big values of h (say bigger than 12). Code:
\p28000 Code:
worktodofile="TestSuite\/6.in"; certificatefile="TestSuite\/6.out"; Code:
maxh = 20; Code:
gp < CHG.GP Reading GPRC: /etc/gprc ...Done. GP/PARI CALCULATOR Version 2.5.1 (released) amd64 running linux (x8664/GMP5.0.5 kernel) 64bit version compiled: Jun 4 2012, gcc4.7.0 (Debian 4.7.011) (readline v6.2 disabled, extended help enabled) Copyright (C) 20002011 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 8000000, primelimit = 500509 *** Warning: new stack size = 134217728 (128.000 Mbytes). realprecision = 28012 significant digits (28000 digits displayed) Welcome to the CHG primality prover!  Input file is: TestSuite/6.in Certificate file is: TestSuite/6.out Found values of n, F and G. Number to be tested has 46877 digits. Modulus has 12581 digits. Modulus is 26.837741491697310904% of n. NOTICE: This program assumes that n has passed a BLS PRPtest with n, F, and G as given. If not, then any results will be invalid! Square test passed for G >> F. Using modified right endpoint. Search for factors congruent to 1. Running CHG with h = 14, u = 6. Right endpoint has 9148 digits. Done! Time elapsed: 33937816ms. Running CHG with h = 14, u = 6. Right endpoint has 8964 digits. Done! Time elapsed: 30500403ms. Running CHG with h = 14, u = 6. Right endpoint has 8599 digits. Done! Time elapsed: 30873974ms. Running CHG with h = 13, u = 5. Right endpoint has 8104 digits. Done! Time elapsed: 18542919ms. Running CHG with h = 13, u = 5. Right endpoint has 7636 digits. Done! Time elapsed: 18322641ms. Running CHG with h = 11, u = 4. Right endpoint has 6893 digits. Done! Time elapsed: 6854132ms. Running CHG with h = 9, u = 3. Right endpoint has 6300 digits. Done! Time elapsed: 2077398ms. Running CHG with h = 9, u = 3. Right endpoint has 5366 digits. Done! Time elapsed: 2016787ms. Running CHG with h = 7, u = 2. Right endpoint has 4025 digits. Done! Time elapsed: 391320ms. Search for factors congruent to n. Running CHG with h = 14, u = 6. Right endpoint has 9148 digits. Done! Time elapsed: 34054669ms. Running CHG with h = 14, u = 6. Right endpoint has 8964 digits. Done! Time elapsed: 31192117ms. Running CHG with h = 14, u = 6. Right endpoint has 8599 digits. Done! Time elapsed: 31922984ms. Running CHG with h = 13, u = 5. Right endpoint has 8104 digits. Done! Time elapsed: 19001912ms. Running CHG with h = 13, u = 5. Right endpoint has 7636 digits. Done! Time elapsed: 18952632ms. Running CHG with h = 11, u = 4. Right endpoint has 6893 digits. Done! Time elapsed: 7182281ms. Running CHG with h = 9, u = 3. Right endpoint has 6301 digits. Done! Time elapsed: 2192084ms. Running CHG with h = 9, u = 3. Right endpoint has 5366 digits. Done! Time elapsed: 2159538ms. Running CHG with h = 7, u = 2. Right endpoint has 4026 digits. Done! Time elapsed: 422691ms. A certificate has been saved to the file: TestSuite/6.out Running David Broadhurst's verifier on the saved certificate... Testing a PRP called "TestSuite/6.in". Pol[1, 1] with [h, u]=[7, 2] has ratio=1.4461419357427070131 E6817 at X, ratio=5.664809224989919335 E8988 at Y, witness=3. Pol[2, 1] with [h, u]=[9, 3] has ratio=7.490470065658087023 E2940 at X, ratio=6.390768475566896671 E4023 at Y, witness=2. Pol[3, 1] with [h, u]=[7, 3] has ratio=1.2972540577360267584 E1584 at X, ratio=5.256884481953367877 E2804 at Y, witness=6449. Pol[4, 1] with [h, u]=[9, 4] has ratio=3.145579049895579619 E593 at X, ratio=9.790444610593665637 E2371 at Y, witness=3. Pol[5, 1] with [h, u]=[10, 5] has ratio=1.0320034758398752235 E2370 at X, ratio=1.2501766403362505471 E3716 at Y, witness=3. Pol[6, 1] with [h, u]=[12, 5] has ratio=7.216621710650853283 E1552 at X, ratio=2.805395746440191462 E2340 at Y, witness=3. Pol[7, 1] with [h, u]=[13, 6] has ratio=5.619243606418243319 E496 at X, ratio=3.1482351295087935110 E2972 at Y, witness=6449. Pol[8, 1] with [h, u]=[13, 6] has ratio=3.1482351295087935110 E2972 at X, ratio=1.5689033180220872231 E2191 at Y, witness=6449. Pol[9, 1] with [h, u]=[14, 6] has ratio=1.6317340876422533882 E1206 at X, ratio=2.4395522529325717148 E1102 at Y, witness=3. Pol[1, 2] with [h, u]=[7, 2] has ratio=1.6068243730474522369 E6818 at X, ratio=1.9558887552173445350 E8986 at Y, witness=17. Pol[2, 2] with [h, u]=[9, 3] has ratio=1.0120641581575526988 E2941 at X, ratio=9.415995163042182551 E4022 at Y, witness=2. Pol[3, 2] with [h, u]=[7, 3] has ratio=1.3268475765018631634 E1584 at X, ratio=2.0407180404974932762 E2803 at Y, witness=3. Pol[4, 2] with [h, u]=[9, 4] has ratio=2.430901089616844084 E593 at X, ratio=3.491959138889946426 E2371 at Y, witness=3. Pol[5, 2] with [h, u]=[10, 5] has ratio=3.680848125044162843 E2371 at X, ratio=2.683030734698952763 E3716 at Y, witness=3. Pol[6, 2] with [h, u]=[12, 5] has ratio=2.7782166245229885464 E1552 at X, ratio=2.2097959611499136744 E2340 at Y, witness=3. Pol[7, 2] with [h, u]=[13, 6] has ratio=5.111982063685797886 E496 at X, ratio=1.7845796163124167244 E2972 at Y, witness=3. Pol[8, 2] with [h, u]=[13, 6] has ratio=1.7845796163124167244 E2972 at X, ratio=7.384962616549326855 E2191 at Y, witness=3. Pol[9, 2] with [h, u]=[14, 6] has ratio=1.4706302622525914306 E1206 at X, ratio=3.827727300991043488 E1102 at Y, witness=23. Validated in 6 sec. Congratulations! n is prime! Goodbye! Last fiddled with by paulunderwood on 20150228 at 11:22 Reason: 25% of N^21 was the wrong thing to say! 

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