This problem requires you to read following scientific article:
Sum of Reciprocals of Germain Primes.
Wagstaff, Samuel S. Journal of Integer Sequences, 24 (2021).
Link: https://cs.uwaterloo.ca/journals/JIS/VOL24/Wagstaff/wag4.pdf
Use the content of the article to work on the problems (a-f) below:
(a) What is the difference between twin primes and Germain primes? Give examples for both.
(b) Which numbers does the set S1,0 represent and what is the value of S
′
1,2
(4 · 1018)?
(c) In the proof of Theorem 1, explain why P
p≤x,p∈Sa,b
1
p =
Px
t=1
πa,b(t)−πa,b(t−1)
t
?
(d) Explain the difference between Table 1 and Table 3.
(e) Use Theorem 3 to calculate an upper bound for π1,16(e
100) in orders of magnitude.
(f) Show in detail why the left- and right-hand side of equation (1) in Theorem 4 are equal.