Primes whose digits sum to a prime

  • Context: Undergrad 
  • Thread starter Thread starter Mooky
  • Start date Start date
  • Tags Tags
    Prime Primes Sum
Click For Summary
SUMMARY

Prime numbers whose digits sum to a prime number are known as "additive primes," a term defined in the OEIS under the entry A046704. The example provided, the prime number 83, sums its digits (8 + 3) to 11, which is also prime. The discussion raises the question of whether there are infinitely many additive primes, a topic that remains open for exploration.

PREREQUISITES
  • Understanding of prime numbers and their properties
  • Familiarity with digit sum calculations
  • Knowledge of the Online Encyclopedia of Integer Sequences (OEIS)
  • Basic number theory concepts
NEXT STEPS
  • Research the properties of additive primes in number theory
  • Explore the OEIS entry A046704 for further examples and sequences
  • Investigate the conjecture regarding the infinitude of additive primes
  • Learn about related concepts such as digital roots and their implications in prime theory
USEFUL FOR

Mathematicians, number theorists, and enthusiasts interested in prime number properties and their relationships with digit sums.

Mooky
Messages
20
Reaction score
0
Is there a name for prime numbers whose digits sum to a prime number? For example, the prime 83 gives 8+3=11, a prime. Is there anything known about these primes, e.g. are there infinitely many of them?

Thanks,
M
 
Mathematics news on Phys.org
OEIS http://oeis.org/A046704 calls these "additive primes" and Google finds others using this name. Perhaps that is enough to start your quest.
 

Similar threads

High School Are All Imaginable Integer Series Necessarily Infinite?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts
  • · Replies 1 ·
Replies
1
Views
2K
MHB Sum of 2 Primes: 45 - (2 Digit Integer)?
  • · Replies 4 ·
Replies
4
Views
2K
Insights The History and Importance of the Riemann Hypothesis
  • · Replies 0 ·
Replies
0
Views
3K
High School Prime Number with Prime Digits
  • · Replies 5 ·
Replies
5
Views
3K
High School Natural Numbers contain all the Primes
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad A question on palindromic primes
  • · Replies 2 ·
Replies
2
Views
1K
MHB Max 3-Digit Prime Divisor of 2000!/(1000!1000!)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Questions regarding Kurepa's Conjecture
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Infinitely many primes of the form p² + nq² -- really?
  • · Replies 8 ·
Replies
8
Views
2K