generalized andrica conjecture
Post on 30-May-2018
227 Views
Preview:
TRANSCRIPT
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 1/11
generali
The An
plotted
Andrica
Similarl
plot it f
It is clea
For
For
Therefo
then sol
biggest
because
Howeve
time re
The exi
Howeve
the valu
and occ
ed Andrica
rica functio
ith mathe
conjecture
y one can c
r .
r that
,
,
e if one con
tions for ea
olution of
it is always
the minimal
r the value
ains unkno
tence of mi
r according
of ,
rs for
conjecture
n
atical softw
ha
nsider the g
.
is neg
is posi
siders the g
ch will o
eneralized
the case that
difference
f the small
wn and its e
imal soluti
to the gener
also known
. If stat
are and for l
s not been y
eneralized
tive, and if
tive, and if
neralized
cur for
ndrica equ
each soluti
between tw
st solution
xistence is u
n of
alized Andr
as the Smar
d as an ine
, where
arge it s
et proven a
ndrica func
ndrica equa
. What
tion
on of gener
consequtiv
f generaliz
nproven.
the generali
ica conjectu
andache co
uality the g
is the n
ems that
d remains a
tion
then
then
tion
is more it is
occurs
lized Andri
e primes is
d Andrica
zed Andrica
re proposed
stant, is
eneralized
prime nu
, ho
n open prob
a
easily prov
for
a equation
at best 2 for
quation
equation is
by Florenti
ndrica conj
(Co
mber can b
wever the
lem.
an
.
.
d solves fo
ble that the
, and for
twin primes
at the pr
still unprov
Smaranda
ecture state
jecture)
.
sent
en.
he
:
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 2/11
for
Numerical plots for the first primes show that the solutions of
tend to be confined in the interval and according to generalized Andrica conjecture
one hopes that this behavior remains true as .
The following plots of were created with Wolfram's Mathematica 5.2, the function
plot range was cut off at , so the edge of the plateau is visualizing the exact
solutions of the equation .
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 3/11
Plots for the first 200 primes. This plot most clearly visualizes the putative minimal solution
known also as the Smarandache constant, which seems to occur for .
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 4/11
Plots for the first 1000 primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 5/11
Plots for the first primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 6/11
Plots for the first primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 7/11
Plots for the first primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 8/11
Plots for the first primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 9/11
Plots for the first primes.
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 10/11
Plots for the first primes.
Anyone with an account can edit this entry. Please help improve it!
"generalized Andrica conjecture" is owned by dankomed.
(view preamble | get metadata)
View style: jsMath HTML reload
Watch:add
See Also: Florentin Smarandache, Smarandache function
Cross-references: plateau, edge, cut, range, Mathematica, interval, inequality, Smarandache constant, Florentin
Smarandache, twin primes, difference, minimal, solutions, equation, positive, negative, clear, open problem,Andrica conjecture, prime number, function
There are 2 references to this entry.
This is version 29 of generalized Andrica conjecture, born on 2007-06-21, modified 2007-07-16.
Object id is 9636, canonical name is GeneralizedAndricaConjecture.
Accessed 1336 times total.
Classification:
8/14/2019 Generalized Andrica Conjecture
http://slidepdf.com/reader/full/generalized-andrica-conjecture 11/11
AMS MSC: 11A41 (Number theory :: Elementary number theory :: Primes)
From PLANETMATH
top related