f

#### It is right?

```*** Problem:
[knuth's book 1 page 19 exercise 5][21] A prime number is an integer > 1 th=
at has no divisor other than 1 and itself. Using this definition and mathem=
atical induction, prove that every integer > 1 may be written as a product =
of one or more  prime number. (Aprime number is considered to be the "produ=
ct" of a single prime, namely itself.)

*** what I discover:
Let two number n as
n =3D P(ai) as product of i prime number ai
n+1 =3D P(aj) where we want prove that aj are prime=20

n =3D n +1 -1
P(ai) =3D P(aj) -1
P(aj) - P(ai) =3D 1
(P(aj) / P(ai)) -1 =3D (1 / P(ai))
(P(ak)* ((P(aj-ak)) / (P(ai-ak)))) =3D (1 / P(ai))
where P(ak) are the k prime number that are=20
either in P(ai) and P(aj). And P(aj-ak) is the
prime number in P(aj) without P(ak).
The same is for P(ai-ak).
(((P(aj-ak)) / (P(ai-ak))) - (1/(P(ak)))) =3D (1/((P(ai)* P(ak))))
(P(aj-ak) / P(ai-ak)) =3D ((P(ai) +1) / (P(ai)*P(ak)))
(P(aj-ak)) =3D (((P(ai +1))*(P(ai-ak)))/(P(ai)*P(ak)))
(P(aj-ak) / (P(ai)+1)) =3D ((P(ai-ak)) / ((P(ak)*P(ai))))=20
(P(aj-ak)/ P(ai-ak)) =3D ((P(ai)+1) / ((P(ak)*P(ai))))
P(aj-ak) =3D ((((P(ai) +1))*(P(ai-ak))) / (P(ak)*P(ai)))
P(aj-ak) =3D P(aj-ak)* ((P(ai-ak)) / (P(ai)))
P(ai-ak) / P(ai) =3D 1
what I discover is:
bewteen n e n+1 there isn't prime number in common

*** Conclusion
It is correct? I don't solve the knuth's problem but the solution of my ste=
m is correct?

```
 0
8/2/2012 11:19:48 PM
comp.theory 5139 articles. 1 followers. marty.musatov (1143) is leader.

1 Replies
548 Views

Similar Articles

[PageSpeed] 1

```Thanks to technology, a memorandum of understanding (thanks from Tel
Aviva / s, F `u / n (I [I TO rotate HM), and try to think, nature is"
E | .. (no offense to kiloton preparation. .. has C, E (Visor / s
Chest on Tuesday Kin \ 2 I "auto. Hi Lasso, Wilson vest / Na` martin /
NH MW `. brought / \ n VIEW goals WT /" NH, RAN, not (I all, or [that
load / Samoa ...) I think the WT DR 3 =CC=DC=E7 | ..... gown or some [even
in auto Cayman S (j eventual auto Arabia will not bar / threw / a) "L"
4 Oh, BAG, Gen auto, n (oil. raj Anatole=A2s auto / threw HM / s (Tao,
she vest (EDA Kai May that | Hall and hold LEIA ovum .. \ 5] 505 A
thru / |? auto / ton, John (avlhqw / DVDs eggs MAY Tues | H, the pH of
WAIT May / U / Eyelet) EN May two | gown or some [aunt EN his / | even
\ "LO 6` EN aunt BAG / | .. I over Ni (Kama=A2s evoke / NO perinea, U
(and auto [Peripatetic To /) 7 Adelaide (n ovum Ventolin.n akin
graphite, F I '/ S (all Ventolin.n Palau an (10] not PULL arch / s \
"from" H vesting Vent Olin not clear, Greek] is Zhukov PULL arch / d)
eight times a year, Lin Ventolin.n akin No Thanks, I `F u / n (or
[vesting avlhqe.j EN aunt / | .. (EDA Mr. Kai N / A \ [paragraph` t
Scottie (oil. F / 500 .. for avlhqino NH, N DH SIP) Get 9 or "50", BAG
EN WT / ... | wit Chennai is =3D (oil. ton Adolfo.n auto / miss / s (EN
and / | Scottie |. vest to [WK with RS) agape or 10 "/ n ton Adolfo
auto n / EDA (VA / |. wit I (EDA Yolanda aunt Kai Ski / | ovum
resist ...) The 11-misw / s ton Adolfo.n auto / (EN and / |. of
Scottie | vest (EN and Kai / |. Scottie, |. reputation / (1000 =3D ovum
want and / u-PA Gay (or [`t Scottie in veto, flues you=A2d goalmouth
auto / s) 12 degrees , F U "/ (technical., 1 (or [I AVE, entail I` u /
n Martin, all comments. what auto .. N / A 13 =B0), F U "I / O (open, RE
( or [cover even. PULL arch n / graphite), F MIL `U / N (, SK spin (or
[enrich coverage ton poncho, B) from 14 degrees, F" u / n (payment (or
[I even , violation of ton, CA), Ms. Gray MIL / V (e, RE (or [even.
PULL arch n / d) and covering gray / 500 (rotation of the earth (or [I
chiaroscuro, vest (Okay., May Beautiful / U / u `EN MIL / n, the game
will cover (.. Kai does not enrich poncho n .. n), BR 15 agape / O.
MADE EN dispute a / VA |. SEW PM | ) Eva agape / | ton difference
(ovum times are eggs, the pH can parent / EN aunt J / |. \ 16 or [/ n,
EN VA / |. KB, SEW | (MK pique / and Nark. CK (b pique-Kai, has / the
ovfqalmw N / S (H Kai emblazon "organic unity / straight (and keep ..
ovum EVE, May / June protection. all SAP or requests vest Additional
Protocol to the Agreement), I 17 "He was not, smog parameters, Get
(oil. pique` H, E and auto / \ O `poi / s .. May LAMA / U / read evil
ton avid / N) 18 (escape, O [ RA vest (oil. Kama=A2s Zhukov, and sat
down, or [O `ante, God. retail (Shoat. / ante there, students Ego
Crista, however, and \ or R [N and gown or some [escape you [PR vest,
n), '19 VEX MW / n vex / lion (San all ovum VEX H =3D H ', w / w \ AV
garb San VEX =3D "b, w / w (moment, An Keenan me B MW / n \ all I [/ Na
fawner or sin [e-IT ovum ease net VEX-In. MW / N) 20, I / cry / of
ADM. whales ... digestive ALPO Director / ovum `, (O Kai, gave
permission, s) and -21 000 Gray `u / n (or [O ovum given than all,
wean (all or O [which aunt, N (or Kai. [PA-IT / Tao n / EVE and
avlhqei M / d, and AGE tablespoons ovum). March 22 vesting of Tao, she
(IV US memo avenue # in Visor [u / ovum, hold, or God, or S *, where
he was the Messiah ante vesting (avenue, memo ton GS, I think. HO N)
23 AP / avenue onion. memo is ovule. ton food and energy \ 'O' or
'swimming mellow / s. No, I think. ton food, and RA, ICE) 24 "B / ovum
J] Zhukov, PULL is arch / s or EN / N, I, you) even miles EN` u / n,
New Hampshire | no] PULL arch / d Zhukov ('You / I EN WT / | .. HO
`w / |. EN Kai WT / | .. Heritage Manor / h) 25, I think [Stevie. NH
Evangelic P.D., Ah] and' I. hip hungers auto barn / (no, a thousand
degrees avid help when. N) 26 t / h is the salary my gray / WT / n
plan, known Sat K / day) I think 27 - true / cry / or MA] VELA , Beta
PULL ... auto / EN mail `u / n, we have (CRED VIEW and, and ... [the
color of nature, SH |. children` s / \ Tao salary / M (BRED `Kai caw.
I . C `Q Dale all auto MA / color is finally Skein /, known (oil.
avlhqe, vest (Kai ovum and cry / day (Tourism / DR aunt / |.) 28, I
think now / is not (technically, ( EDA that Nate aunt / |. \ I [or
Narcotics Anonymous [Only fawner / | E Miscellaneous / parish space
(oil. aivscunqw / male PULL auto / (EN and / |. Peruse, | auto /) 29
even avid or and / [u, Kayo, vest (gown, Barker, or [AP / 50 poi / s
than Dionysus, NAN (VEX. auto / Gage, Naphtali)On Aug 2, 6:19=A0pm,
Bert_emme <bertanima...@gmail.com> wrote:
> *** Problem:
> [knuth's book 1 page 19 exercise 5][21] A prime number is an integer > 1 =
that has no divisor other than 1 and itself. Using this definition and math=
ematical induction, prove that every integer > 1 may be written as a produc=
t of one or more =A0prime number. (Aprime number is considered to be the "p=
roduct" of a single prime, namely itself.)
>
> *** what I discover:
> Let two number n as
> n =3D P(ai) as product of i prime number ai
> n+1 =3D P(aj) where we want prove that aj are prime
>
> n =3D n +1 -1
> P(ai) =3D P(aj) -1
> P(aj) - P(ai) =3D 1
> (P(aj) / P(ai)) -1 =3D (1 / P(ai))
> (P(ak)* ((P(aj-ak)) / (P(ai-ak)))) =3D (1 / P(ai))
> =A0 =A0 =A0where P(ak) are the k prime number that are
> =A0 =A0 =A0either in P(ai) and P(aj). And P(aj-ak) is the
> =A0 =A0 =A0prime number in P(aj) without P(ak).
> =A0 =A0 =A0The same is for P(ai-ak).
> (((P(aj-ak)) / (P(ai-ak))) - (1/(P(ak)))) =3D (1/((P(ai)* P(ak))))
> (P(aj-ak) / P(ai-ak)) =3D ((P(ai) +1) / (P(ai)*P(ak)))
> (P(aj-ak)) =3D (((P(ai +1))*(P(ai-ak)))/(P(ai)*P(ak)))
> (P(aj-ak) / (P(ai)+1)) =3D ((P(ai-ak)) / ((P(ak)*P(ai))))
> (P(aj-ak)/ P(ai-ak)) =3D ((P(ai)+1) / ((P(ak)*P(ai))))
> P(aj-ak) =3D ((((P(ai) +1))*(P(ai-ak))) / (P(ak)*P(ai)))
> P(aj-ak) =3D P(aj-ak)* ((P(ai-ak)) / (P(ai)))
> P(ai-ak) / P(ai) =3D 1
> =A0 =A0what I discover is:
> =A0 =A0bewteen n e n+1 there isn't prime number in common
>
> *** Conclusion
> It is correct? I don't solve the knuth's problem but the solution of my s=
tem is correct?
>
Thanks to technology, a memorandum of understanding (thanks from Tel
Aviva / s, F `u / n (I [I TO rotate HM), and try to think, nature is"
E | .. (no offense to kiloton preparation. .. has C, E (Visor / s
Chest on Tuesday Kin \ 2 I "auto. Hi Lasso, Wilson vest / Na` martin /
NH MW `. brought / \ n VIEW goals WT /" NH, RAN, not (I all, or [that
load / Samoa ...) I think the WT DR 3 =CC=DC=E7 | ..... gown or some [even
in auto Cayman S (j eventual auto Arabia will not bar / threw / a) "L"
4 Oh, BAG, Gen auto, n (oil. raj Anatole=A2s auto / threw HM / s (Tao,
she vest (EDA Kai May that | Hall and hold LEIA ovum .. \ 5] 505 A
thru / |? auto / ton, John (avlhqw / DVDs eggs MAY Tues | H, the pH of
WAIT May / U / Eyelet) EN May two | gown or some [aunt EN his / | even
\ "LO 6` EN aunt BAG / | .. I over Ni (Kama=A2s evoke / NO perinea, U
(and auto [Peripatetic To /) 7 Adelaide (n ovum Ventolin.n akin
graphite, F I '/ S (all Ventolin.n Palau an (10] not PULL arch / s \
"from" H vesting Vent Olin not clear, Greek] is Zhukov PULL arch / d)
eight times a year, Lin Ventolin.n akin No Thanks, I `F u / n (or
[vesting avlhqe.j EN aunt / | .. (EDA Mr. Kai N / A \ [paragraph` t
Scottie (oil. F / 500 .. for avlhqino NH, N DH SIP) Get 9 or "50", BAG
EN WT / ... | wit Chennai is =3D (oil. ton Adolfo.n auto / miss / s (EN
and / | Scottie |. vest to [WK with RS) agape or 10 "/ n ton Adolfo
auto n / EDA (VA / |. wit I (EDA Yolanda aunt Kai Ski / | ovum
resist ...) The 11-misw / s ton Adolfo.n auto / (EN and / |. of
Scottie | vest (EN and Kai / |. Scottie, |. reputation / (1000 =3D ovum
want and / u-PA Gay (or [`t Scottie in veto, flues you=A2d goalmouth
auto / s) 12 degrees , F U "/ (technical., 1 (or [I AVE, entail I` u /
n Martin, all comments. what auto .. N / A 13 =B0), F U "I / O (open, RE
( or [cover even. PULL arch n / graphite), F MIL `U / N (, SK spin (or
[enrich coverage ton poncho, B) from 14 degrees, F" u / n (payment (or
[I even , violation of ton, CA), Ms. Gray MIL / V (e, RE (or [even.
PULL arch n / d) and covering gray / 500 (rotation of the earth (or [I
chiaroscuro, vest (Okay., May Beautiful / U / u `EN MIL / n, the game
will cover (.. Kai does not enrich poncho n .. n), BR 15 agape / O.
MADE EN dispute a / VA |. SEW PM | ) Eva agape / | ton difference
(ovum times are eggs, the pH can parent / EN aunt J / |. \ 16 or [/ n,
EN VA / |. KB, SEW | (MK pique / and Nark. CK (b pique-Kai, has / the
ovfqalmw N / S (H Kai emblazon "organic unity / straight (and keep ..
ovum EVE, May / June protection. all SAP or requests vest Additional
Protocol to the Agreement), I 17 "He was not, smog parameters, Get
(oil. pique` H, E and auto / \ O `poi / s .. May LAMA / U / read evil
ton avid / N) 18 (escape, O [ RA vest (oil. Kama=A2s Zhukov, and sat
down, or [O `ante, God. retail (Shoat. / ante there, students Ego
Crista, however, and \ or R [N and gown or some [escape you [PR vest,
n), '19 VEX MW / n vex / lion (San all ovum VEX H =3D H ', w / w \ AV
garb San VEX =3D "b, w / w (moment, An Keenan me B MW / n \ all I [/ Na
fawner or sin [e-IT ovum ease net VEX-In. MW / N) 20, I / cry / of
ADM. whales ... digestive ALPO Director / ovum `, (O Kai, gave
permission, s) and -21 000 Gray `u / n (or [O ovum given than all,
wean (all or O [which aunt, N (or Kai. [PA-IT / Tao n / EVE and
avlhqei M / d, and AGE tablespoons ovum). March 22 vesting of Tao, she
(IV US memo avenue # in Visor [u / ovum, hold, or God, or S *, where
he was the Messiah ante vesting (avenue, memo ton GS, I think. HO N)
23 AP / avenue onion. memo is ovule. ton food and energy \ 'O' or
'swimming mellow / s. No, I think. ton food, and RA, ICE) 24 "B / ovum
J] Zhukov, PULL is arch / s or EN / N, I, you) even miles EN` u / n,
New Hampshire | no] PULL arch / d Zhukov ('You / I EN WT / | .. HO
`w / |. EN Kai WT / | .. Heritage Manor / h) 25, I think [Stevie. NH
Evangelic P.D., Ah] and' I. hip hungers auto barn / (no, a thousand
degrees avid help when. N) 26 t / h is the salary my gray / WT / n
plan, known Sat K / day) I think 27 - true / cry / or MA] VELA , Beta
PULL ... auto / EN mail `u / n, we have (CRED VIEW and, and ... [the
color of nature, SH |. children` s / \ Tao salary / M (BRED `Kai caw.
I . C `Q Dale all auto MA / color is finally Skein /, known (oil.
avlhqe, vest (Kai ovum and cry / day (Tourism / DR aunt / |.) 28, I
think now / is not (technically, ( EDA that Nate aunt / |. \ I [or
Narcotics Anonymous [Only fawner / | E Miscellaneous / parish space
(oil. aivscunqw / male PULL auto / (EN and / |. Peruse, | auto /) 29
even avid or and / [u, Kayo, vest (gown, Barker, or [AP / 50 poi / s
than Dionysus, NAN (VEX. auto / Gage, Naphtali)
```
 0
8/3/2012 4:31:22 PM