Update README.md

code/README.md

@@ -43,7 +43,7 @@ The program "searchpm.cc" is searching the smallest (probable) prime in simple f
 
 The program "searchp1.cc" is searching the smallest (probable) prime in simple families extensively, starting with length 1000.
 
-The program "searchLLR.cc" is a sieving (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html) program like *SRSIEVE* (https://www.bc-team.org/app.php/dlext/?cat=3, http://web.archive.org/web/20160922072340/https://sites.google.com/site/geoffreywalterreynolds/programs/, http://www.rieselprime.de/dl/CRUS_pack.zip, https://primes.utm.edu/bios/page.php?id=905, https://www.rieselprime.de/ziki/Srsieve, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/srsieve_1.1.4, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/sr1sieve_1.4.6, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/sr2sieve_2.0.0, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/srbsieve, https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/mtsieve_2.4.1/srsieve2.exe, https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/mtsieve_2.4.1/srsieve2cl.exe) but only sieved to the prime 130337 (while *SRSIEVE* usually sieve to 10<sup>9</sup> or more) and not remove the numbers with algebraic factors (see https://mersenneforum.org/showpost.php?p=452132&postcount=66 and https://mersenneforum.org/showthread.php?t=21916 and https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c (note: for the sequence (*a*×*b*<sup>*n*</sup>+*c*)/*gcd*(*a*+*c*,*b*−1), the case of "Mersenne number" in https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c is the case which *a* is rational power of *b*, *c* = −1 and the case which *a* is rational power of *b*, *c* = 1, *gcd*(*a*+*c*,*b*−1) ≥ 3, and the case of "GFN" in https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c is the case which *a* is rational power of *b*, *c* = 1, *gcd*(*a*+*c*,*b*−1) is either 1 or 2)), and the program "searchLLR.cc" prints the *LLR* (http://jpenne.free.fr/index2.html, https://primes.utm.edu/bios/page.php?id=431, https://www.rieselprime.de/ziki/LLR, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403win64, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403linux64) input file and thus the *LLR* program must be used after the program "searchLLR.cc".
+The program "searchLLR.cc" is a sieving (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html, http://www.rechenkraft.net/yoyo/y_status_sieve.php) program like *SRSIEVE* (https://www.bc-team.org/app.php/dlext/?cat=3, http://web.archive.org/web/20160922072340/https://sites.google.com/site/geoffreywalterreynolds/programs/, http://www.rieselprime.de/dl/CRUS_pack.zip, https://primes.utm.edu/bios/page.php?id=905, https://www.rieselprime.de/ziki/Srsieve, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/srsieve_1.1.4, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/sr1sieve_1.4.6, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/sr2sieve_2.0.0, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/srbsieve, https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/mtsieve_2.4.1/srsieve2.exe, https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/mtsieve_2.4.1/srsieve2cl.exe) but only sieved to the prime 130337 (while *SRSIEVE* usually sieve to 10<sup>9</sup> or more) and not remove the numbers with algebraic factors (see https://mersenneforum.org/showpost.php?p=452132&postcount=66 and https://mersenneforum.org/showthread.php?t=21916 and https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c (note: for the sequence (*a*×*b*<sup>*n*</sup>+*c*)/*gcd*(*a*+*c*,*b*−1), the case of "Mersenne number" in https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c is the case which *a* is rational power of *b*, *c* = −1 and the case which *a* is rational power of *b*, *c* = 1, *gcd*(*a*+*c*,*b*−1) ≥ 3, and the case of "GFN" in https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/srsieve_1.1.4/algebraic.c is the case which *a* is rational power of *b*, *c* = 1, *gcd*(*a*+*c*,*b*−1) is either 1 or 2)), and the program "searchLLR.cc" prints the *LLR* (http://jpenne.free.fr/index2.html, https://primes.utm.edu/bios/page.php?id=431, https://www.rieselprime.de/ziki/LLR, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403win64, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403linux64) input file and thus the *LLR* program must be used after the program "searchLLR.cc".
 
 There is also a *Pari*/*GP* (https://pari.math.u-bordeaux.fr/) program code to compute the first few minimal primes (say < 2<sup>32</sup>) in base *b* (this program looks at all primes one by one, to test whether a prime is a minimal prime or not, and has time complexity (https://en.wikipedia.org/wiki/Time_complexity) *O*(*n*) when compute the minimal primes ≤ *n* (where *O* is the big *O* notation (https://en.wikipedia.org/wiki/Big_O_notation, https://primes.utm.edu/glossary/xpage/BigOh.html, https://mathworld.wolfram.com/Big-ONotation.html)), thus this program would need a time longer than the age of the universe (https://en.wikipedia.org/wiki/Age_of_the_universe) to test to the largest minimal prime for base *b* = 10 (i.e. 5000000000000000000000000000027), even if we can test 10<sup>6</sup> primes per second (https://en.wikipedia.org/wiki/Second)), hence to do this is impractically, not to mention base *b* = 24, whether the set of the C++ programs in this page has time complexity (https://en.wikipedia.org/wiki/Time_complexity) *O*(*log*(*n*)<sup>3</sup>) (where *log* is the natural logarithm (https://en.wikipedia.org/wiki/Natural_logarithm, https://primes.utm.edu/glossary/xpage/Log.html, https://mathworld.wolfram.com/NaturalLogarithm.html)) when compute the minimal primes ≤ *n*, thus it has a polynomial time (https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time, https://mathworld.wolfram.com/PolynomialTime.html)):