Qm
Brainteasers

Can the average of two consecutive primes be prime?

numbersprimeslogic

Take any two consecutive primes, meaning two primes with no other prime between them, such as 7 and 11 or 23 and 29.

Can their average ever be a prime number? Give a proof, and handle every case, including the smallest primes.

Show a hint

Where does the average of two different numbers lie in relation to the two numbers?

Your answer

Solving needs a free account

Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.

Create a free accountSign in

Discussion

Sign in to join the discussion · reading is open to everyone

💡 Discussion rules

  1. No full solutions here. Hints and approaches only.
  2. Complexity, edge cases and intuition are the point.
  3. Interview experiences are welcome. Respect your NDAs.

Loading discussion…

Learn the concepts

The theory behind this question.

Cheryl's Birthday and Iterated KnowledgeLogic and QuantifiersOne Question, Two Guards, One DoorProof Techniques: Direct, Contrapositive, ContradictionAdaptive Versus Pre-Committed Weighing Strategies

Related questions

Why one less than a prime's square is always a multiple of 24The number that describes its own digitsTwo primes that add up to 101Writing 100 as a sum of consecutive numbersA sentence nobody on the island can say
All questions →