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Augusto Santi
Augusto Santi
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I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

If the previous was true, the density of such primes in the whole set of prime numbers would be comparable to that of primes inside the set of naturals.

I ask if this estimate is correct and some references about this matter.

Thanks.

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

Thanks.

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$

If the previous was true, the density of such primes in the whole set of prime numbers would be comparable to that of primes inside the set of naturals.

I ask if this estimate is correct and some references about this matter.

Thanks.

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edit approved Mar 3, 2020 at 19:28
user153001
edit approved Mar 3, 2020 at 19:28
user153001

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

Thanks.

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

Thanks.

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

Thanks.

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Augusto Santi
Augusto Santi
  • 1k
  • 5
  • 17

About the number of primes which are the sum of 3 consecutive primes (OEIS A034962)

I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes (OEIS A034962), that is for instance: $$5+7+11=23$$ $$7+11+13=31$$ $$11+13+17=41$$ $$17+19+23=59$$ $$19+23+29=71$$ $$23+29+31=83$$ $$29+31+37=97$$ $$...$$ The number of such triplets, till a certain integer n, seems to be well approximated by the following function: $$\frac{e\cdot\pi(n)}{\log(n)}$$ I ask if this estimate is correct and some references about this matter.

Thanks.