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Twin prime conjecture proof (Lagarias)

I’m studying the proof of the Twin prime conjecture at the moment. This proof is provided in C.Lagarias’ book: “Computational number theory”.
The given proof is based on this comment:
But this looks a little bit ugly to me. I’m not a good student in number theory, so I need an explanation on the the following points:
1.At one point it’s explained that we can change the summation “by the rule $a_m = a_{2^n m}$” and then it’s proven to be true that $\sum_{n \leq k} a_n = \sum_{n \leq k} a_{2^n}$.
2.The authors first use the formula $\sum_{k=1}^p\,\varphi(2^k) = 2\cdot \prod_{p \mid 2^p} (1-\frac{1}{p})$ and then $\varphi(q_1q_2) = \varphi(q_1)\varphi(q_2)$ is stated with $q_1q_2 = 2^{2^n}$.
3.At the end of the proof it’s given that the summation on the left hand side equals $\frac{3}{4}\cdot k!$ and that the summation on the right hand side equals $\frac{3}{4} \cdot (k-1)! \cdot \prod_{p \mid k}(1-\frac{1}{p})$ so both summations should be equal.
4.Explaining a little bit the proof is a little bit difficult, since I don

Translation of â€˜Alfaz al-Qur’an al-Kareemâ€™ in Urdu PDF. pdf Urdu download to your computer in four different fonts.

Al Mu’jam al Mufahras li Alfaz al Qur’an al Kareem PDF download;Lectures – Book and Lecture Number Ayatul Qurbana PDF. ALLAH’S BOOK IN PERFECT TEXTS-QUR’AN.
Mixing names of some books that is prohibited in Islam.. there are also limited options in Indonesian version of the book. Latest Urdu grammar urdu language books and literature books in PDF Free ebook you can download and view any time 24/7. Al Mu’jam Al Mufahras li Alfaz al Qur’an al Kareem al Mu’jam al Mufahras li al Qur’an al Kareem: PDF

Urdu Translation of Holy Quran-Mu’jam ul Mu’ajama li al-Quran al-Kareem – PDF

Size: 3.22 MB – Pages: 4212. – Urdu translation of the holy Quran by Ustaad MQ. A.H. FaizulAzam. – Download Urdu.
Mu’jam ul Quran Arabic New version of Urdu translation of Quran – Mu’jam al Aqlan – PDF. Mu’jam. Mu’jam al Quran Arabic is one of the famous books written by Mufti Syed Sahib Abbas Shirazi.

Al Mu’jam Al Mufahras li Alfaz al Qur’an al Kareem PDF download;

Download Islam in English as PDF Ebook. pdf in PDF format to your computer in four different fonts. PDF download to your computer in four different fonts. Al Mu’jam Al Mufahras li alfaz al Qur’an al Kareem. 20.12.2007 · Learning.to
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