Erdős Problem #409 — How many iterations of $n\mapsto \phi(n)+1$ are needed before a prime is reached?

At least 45 years old · documented by 1980

How many iterations of $n\mapsto \phi(n)+1$ are needed before a prime is reached? Can infinitely many $n$ reach the same prime? What is the density of $n$ which reach any fixed prime?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

iterated-functions number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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