Prime numbers and primality testing Yahoo Group AP19 starting with 19 =============================================== Jaroslaw Wroblewski Message 1 of 6 Feb 25, 2013 ----------------------------------------------- Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: 19 + 13234551541698967679 * 17# * n, n=0,...,18 (27 digits) At the moment it is not known whether the difference of the AP is the smallest possible, but Wojciech is working to determine that. Although Wojciech was using the ideas I have developed in the past, he created brand new implementation of the search program on his own. Jarek =============================================== mikeoakes2 Message 2 of 6 Feb 26, 2013 ----------------------------------------------- --- In primenumbers@yahoogroups.com, Jaroslaw Wroblewski wrote: > > Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: > > 19 + 13234551541698967679 * 17# * n, n=0,...,18 > (27 digits) > An amazing and highly nontrivial discovery - many congratulations! But don't rush to look for an AP23: heuristics in my NMBRTHRY post of 2001 https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0106&L=NMBRTHRY&F=&S=&P=3812 indicate that a complete search would take many times the age of the Universe. Mike =============================================== Jens Kruse Andersen Message 3 of 6 Feb 27, 2013 ----------------------------------------------- Jaroslaw Wroblewski wrote: > Wojciech Izykowski has discovered AP19 with the smallest possible start of > 19: > > 19 + 13234551541698967679 * 17# * n, n=0,...,18 > (27 digits) > > At the moment it is not known whether the difference of the AP is the > smallest possible, but Wojciech is working to determine that. Congratulations to Wojciech! http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is updated with a mixed color entry to show that it has the smallest possible start but the difference may not be the smallest. -- Jens Kruse Andersen =============================================== Jaroslaw Wroblewski Message 4 of 6 Apr 5, 2013 ----------------------------------------------- Wojciech Izykowski has discovered AP19 with the smallest possible start of 19 and a smaller difference than in his first example: 19 + 4244193265542951705 * 17# * n, n=0,...,18 (26 digits) He needs about a week to determine whether this difference is the smallest possible. Jarek 2013/2/26 Jaroslaw Wroblewski : > Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: > > 19 + 13234551541698967679 * 17# * n, n=0,...,18 > (27 digits) > > At the moment it is not known whether the difference of the AP is the > smallest possible, but Wojciech is working to determine that. > > Although Wojciech was using the ideas I have developed in the past, he > created brand new implementation of the search program on his own. > > Jarek =============================================== Jaroslaw Wroblewski Message 5 of 6 Apr 10, 2013 ----------------------------------------------- 2013/4/5 Jaroslaw Wroblewski : > Wojciech Izykowski has discovered AP19 with the smallest possible > start of 19 and a smaller difference than in his first example: > > 19 + 4244193265542951705 * 17# * n, n=0,...,18 > (26 digits) Wojciech has completed his computations and confirmed that the above AP19 has the smallest possible diffrence among all AP19 starting with 19. Jarek =============================================== Jens Kruse Andersen Message 6 of 6 Apr 10, 2013 ----------------------------------------------- Jaroslaw Wroblewski wrote: >> 19 + 4244193265542951705 * 17# * n, n=0,...,18 > > Wojciech has completed his computations and confirmed that the above > AP19 has the smallest possible diffrence among all AP19 starting with > 19. Congratulations to Wojciech. http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is updated so the color is no longer red. It should also be submitted to http://oeis.org/A061558 -- Jens Kruse Andersen =============================================== Cached by Georg Fischer at Nov 14 2019 12:47 with clean_yahoo.pl V1.4