Using Bertrand's postulate which states: For every integer n &#x2265;<!-- ≥ --> 1 ther

Landon Mckinney

Landon Mckinney

Answered question

2022-05-07

Using Bertrand's postulate which states:
For every integer n 1 there is a prime number p such that n < p 2 n
Prove that there exists infinitely many primes whose decimal expansion starts with 1.
I'm guessing I need to use something equal to 10 in this as it is a decimal expansion, but I'm not seeing where to start?
Any guidance would be great, thank you

Answer & Explanation

exorteygrdh

exorteygrdh

Beginner2022-05-08Added 16 answers

Just take the sequence a n = 10 n . Since for n > 1, we have n < p < 2 n, so there is a prime between a n , 2 a n but all numbers in between begin with 1.

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