## Adding and Subtracting the First n Prime Numbers to Get the Next Prime Number

In this post I want to present the following conjecture related to odd-indexed prime numbers (see OEIS sequence A031368): All the odd-indexed prime numbers larger than 2 can be obtained from all the previous prime numbers using addition and subtraction. The conjecture was inspired by Curiosa 67 from Scripta Mathematica ( page 159, Volume 7,… Continue reading Adding and Subtracting the First n Prime Numbers to Get the Next Prime Number

## Adding and Subtracting 1 and the First n Primes to Get the Next Prime (Part 2)

In part 1 I dealt with even-indexed primes. In this post I want to show the first few examples of how to obtain the odd-indexed prime numbers using the addition or subtraction of 1 and all the other preceding primes. The odd-indexed primes are covered by the OEIS sequence A031368. The summation for each prime… Continue reading Adding and Subtracting 1 and the First n Primes to Get the Next Prime (Part 2)

## Adding and Subtracting 1 and the First n Primes to Get the Next Prime (Part 1)

In this post I want to show a few examples of how a prime number can be obtained from all the preceding prime numbers and 1 using addition and subtraction. In Part 1 I’ll deal with only even-indexed primes: a(n)=prime(2n). 3 is the first even-indexed prime, 7 is the second, 13 is the third, 19… Continue reading Adding and Subtracting 1 and the First n Primes to Get the Next Prime (Part 1)

## A Prime Counting Sequence and Andrica’s Conjecture

In this post I want to discuss a prime counting sequence similar to OEIS sequence A066888. The sequence A066888 counts the number of primes between 2 consecutive triangular numbers. On the OEIS page of the sequence there is a conjecture that says that there is at least one prime number between 2 consecutive triangular numbers.… Continue reading A Prime Counting Sequence and Andrica’s Conjecture