Fdtxjr

Accidentally leaked the solution to an assignment, what to do now? (I'm the prof)

Set-theoretical foundations of Mathematics with only bounded quantifiers

Email Account under attack (really) - anything I can do?

How can I automatically replace [[ and ]] with the [LeftDoubleBracket] and [RightDoubleBracket] operators?

How did the USSR manage to innovate in an environment characterized by government censorship and high bureaucracy?

"You are your self first supporter", a more proper way to say it

How old can references or sources in a thesis be?

Why has Russell's definition of numbers using equivalence classes been finally abandoned? ( If it has actually been abandoned).

Why Is Death Allowed In the Matrix?

"which" command doesn't work / path of Safari?

Motorized valve interfering with button?

If Manufacturer spice model and Datasheet give different values which should I use?

Example of a relative pronoun

Prevent a directory in /tmp from being deleted

Can I make popcorn with any corn?

Draw simple lines in Inkscape

Pronouncing Dictionary.com's W.O.D "vade mecum" in English

Japan - Plan around max visa duration

What defenses are there against being summoned by the Gate spell?

Continuity at a point in terms of closure

DOS, create pipe for stdin/stdout of command.com(or 4dos.com) in C or Batch?

Why are 150k or 200k jobs considered good when there are 300k+ births a month?

When blogging recipes, how can I support both readers who want the narrative/journey and ones who want the printer-friendly recipe?

What would the Romans have called "sorcery"?

Prove that $forall m in mathbbN^*,exists n in mathbbN,forall k geq n, p_k+1^m

Is it true that $sum_k=1^n(p_kprod_i=1^k(1-p_i)) stackrelmbox?= 1 - prod_i=1^n(1-p_i)$Estimate for the product of primes less than nProve or disprove that $forall kinmathbb N$ there exist tree consecutive primes such that $p_i-p_i-1gt k$ and $p_i+1-p_igt k$Inequality with Euler's totient functionProve if $n=p_1p_2cdots p_k +1$, then for every $i$, $i=1,2,cdots k, p_i$ does not divide n.Prove that $prod_i<j (p_i^p_j-p_j^p_i)$ is divisible by $5777$Prove $prod_c < p leq x left(1 - fraccp right) ll log ^-c x .$Prove that $forall xinmathbbN text there always exists a prime pequiv1 pmod 6 text s.t. p|(2x)^2+3;$Interesting missing proof (Prime Number Theorem)Weak k-Tuple conjecture form and what we should proof

1

$begingroup$

I need to prove :

$$forall m in mathbbN^*,exists n in mathbbN,forall k geq n, p_k+1^m<prod_i=1^kp_i$$

I can prove this assertion using Prime number theorem :

For fixed $m$ we have : $logleft(displaystyle prod_i=1^kp_i right) sim p_k$ and $log(p_k+1) sim log(k+1)$ give the result.

But I need another proof not asymptotic.

number-theory elementary-number-theory prime-numbers arithmetic

share|cite|improve this question

edited Mar 22 at 18:35

LAGRIDA

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Bertrand postulate?
  $endgroup$
  – Collag3n
  Mar 22 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Betrand postulate gives $p_i < p_i+1 < 2p_i$. But the question is about $p_k+1$ and the primorial of $p_k$
  $endgroup$
  – LAGRIDA
  Mar 22 at 10:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Bertrand postulate gives $p_i < 2^i implies p_k+1^m < 2^m(k+1)$ and if we can proove $2^m(k+1) < displaystyle prod_i=1^kp_i$ for some $k geq n$
  $endgroup$
  – LAGRIDA
  Mar 22 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  We have $2^leftlfloor log(p_i)/log(2) rightrfloor leq p_i$
  $endgroup$
  – LAGRIDA
  Mar 22 at 11:15
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can someone explain why the downvote
  $endgroup$
  – HAMIDINE SOUMARE
  Mar 22 at 14:18
  

  
  
  
  

 | 
show 5 more comments

1

$begingroup$

I need to prove :

$$forall m in mathbbN^*,exists n in mathbbN,forall k geq n, p_k+1^m<prod_i=1^kp_i$$

I can prove this assertion using Prime number theorem :

For fixed $m$ we have : $logleft(displaystyle prod_i=1^kp_i right) sim p_k$ and $log(p_k+1) sim log(k+1)$ give the result.

But I need another proof not asymptotic.

number-theory elementary-number-theory prime-numbers arithmetic

share|cite|improve this question

edited Mar 22 at 18:35

LAGRIDA

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Bertrand postulate?
  $endgroup$
  – Collag3n
  Mar 22 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Betrand postulate gives $p_i < p_i+1 < 2p_i$. But the question is about $p_k+1$ and the primorial of $p_k$
  $endgroup$
  – LAGRIDA
  Mar 22 at 10:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Bertrand postulate gives $p_i < 2^i implies p_k+1^m < 2^m(k+1)$ and if we can proove $2^m(k+1) < displaystyle prod_i=1^kp_i$ for some $k geq n$
  $endgroup$
  – LAGRIDA
  Mar 22 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  We have $2^leftlfloor log(p_i)/log(2) rightrfloor leq p_i$
  $endgroup$
  – LAGRIDA
  Mar 22 at 11:15
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can someone explain why the downvote
  $endgroup$
  – HAMIDINE SOUMARE
  Mar 22 at 14:18
  

  
  
  
  

 | 
show 5 more comments

$begingroup$

I need to prove :

$$forall m in mathbbN^*,exists n in mathbbN,forall k geq n, p_k+1^m<prod_i=1^kp_i$$

I can prove this assertion using Prime number theorem :

For fixed $m$ we have : $logleft(displaystyle prod_i=1^kp_i right) sim p_k$ and $log(p_k+1) sim log(k+1)$ give the result.

But I need another proof not asymptotic.

number-theory elementary-number-theory prime-numbers arithmetic

share|cite|improve this question

edited Mar 22 at 18:35

LAGRIDA

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

$endgroup$

share|cite|improve this question

edited Mar 22 at 18:35

LAGRIDA

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

share|cite|improve this question

edited Mar 22 at 18:35

LAGRIDA

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112

asked Mar 22 at 8:23

LAGRIDALAGRIDA

270112