(1). Announcement of latest findings.
This is the Homepage for full Goldbach's Sequence
Hunt. Since both the Webpage and the definition of Goldbach's sequence are
new, we are just at the beginning of the hunt. Ultimately, the hunt will be as
difficult as the Mersenne Hunt when very lengthy multiple precision computations
will be required. So, join the hunt early and get your names entered into our
record book. The game has been designed to suit both nerds and nonnerds.
We wish you happy GS hunting.
A verified full Goldbach's sequence is announced in the following format:
GS1(7):0
This means that the full Goldbach's Sequence
found by the square of a contiguous prime sequence starting from 3 to 7,
i.e. the prime set (3,5,7) has been found. GS1 means that the even terms
in the Goldbach's Sequence ranges from 6 to 2*p where p is the largest prime
in the prime set. GS2 covers a shorter range from 6 to p+3. The zero behind
the colon signifies the number of missing even terms in the Goldbach's
sequence. Currently, the followings have been found and verified:
GS(3):0,GS(5):0,GS(7):0,GS(13):0,GS(19):0, and GS(109):0.
This section will be updated monthly if there are new
announcements at the end of the month. For the month of February (ending on
28.2.97) the following findings have been reported. The search range has been
twice extended when each time it was broken within days. The present range is
now fixed from 109 to 1000_000_000_000. So far no full GS has been discovered
above GS1(109):0. The next full GS1 or GS2 is awaiting to be discovered!! Will
your name be permanently associated with a new GS?
Every GS found will be recorded with the finders' name. After
announcements, these findings will be transferred to the archive section of this Homepage.
Here are the latest announcements.
(1a) No full GS1 has been found between 109 and 1_000_000.
(1b) No full GS1 has been found between 1_000_000 and 10_000_000.
(1c) No full GS1 has been found between 10_000_000 and 100_000_000.
Finder: Guillermo Ballester Valor,
Granada (SPAIN),
E-mail: gbv@ctv.es
(2a) Below 1_000_000 the"Incomplete Goldbach's Sequence with the largest number of missing even terms" is for prime 668509 which has 209 missing even terms, i.e. 3.126*10^-4%:
(2b) Below 1_000_000 the"Incomplete Goldbach's Sequence with the smallest percentage of missing even terms" is for prime 783803 which has 12 missing even terms, i.e. 1.531*10^-5%:
(2c) No full GS1 has been discovered between 109 and 1_000_000_000.
(2d) Below 1_000_000_000 the "Incomplete Goldbach's Sequence with the largest number of missing even terms" is prime 866957599 which has 607 missing terms i.e.
(2e) Below 1_000_000_000 the "Incomplete Goldbach's Sequence with the smallest percentage of missing even terms" is prime 978469127 which has 26 missing terms i.e. 2.657*10^-6%
Finder: Vincent Celier (current record holder),
Richmond, B.C., CANADA,
E-mail: vcelier@direct.ca