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On a conjecture on shifted primes with large prime factors

Bulletin of the Australian Mathematical Society, 2022
Let $$\mathcal {P}$$ P be the set of all primes and $$\pi (x)$$ π ( x ) be the number of primes up to x . For any $$n\ge 2$$ n ≥ 2 , let $$P^+(n)$$ P + ( n ) be the largest prime factor of n .
Yuchen Ding
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On shifted primes with large prime factors and their products [PDF]

Archiv der Mathematik, 2018
The author gives partial answers to two questions on shifted primes with large prime factors. To state these results let us start with some definitions. \textit{F. Luca} et al. [Bull. Belg. Math. Soc. - Simon Stevin 22, No. 1, 39--47 (2015; Zbl 1370.11110)] considered the following counting function: \[T_{\theta}(x):= |\{p\leq x: P^+(p-1)\geq p^{\theta}
Jie Wu
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The polynomial multidimensional Szemerédi Theorem along shifted primes [PDF]

Israel Journal of Mathematics, 2010
If $\vec q_1 ,...,\vec q_m $ : ℤ → ℤℓ are polynomials with zero constant terms and E ⊂ ℤℓ has positive upper Banach density, then we show that the set E ∩ (E − $\vec q_1 $ (p − 1)) ∩ … ∩ (E − $\vec q_m $ (p − 1)) is nonempty for some prime p.
N. Frantzikinakis, B. Host, Bryna Kra
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Shifted-Prime Factorizations

The American Mathematical Monthly, 1981
Kenneth H. Rosen
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On the largest prime factor of shifted primes

Acta Mathematica Sinica, English Series, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng-Juan Chen, Yong Gao Chen
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Prime Divisors of Shifted Factorials

Bulletin of the London Mathematical Society, 2005
For any positive integer n we let $P(n)$ be the largest prime factor of n . We improve and generalize several results of P. Erdős and C. Stewart on $P(n!+1)$ . In particular, we show that $\limsup_{n \to \infty}P(n!+1)/n \ge 2.5$ , which improves their lower bound of $\limsup_{n \to \infty} P(n!+1)/n >2$ .
F. Luca, I. Shparlinski
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If small molecules immunotherapy comes, can the prime be far behind?

European journal of medicinal chemistry, 2021
Anti-cancer immunotherapy, which includes cellular immunotherapy, immune checkpoint inhibitors and cancer vaccines, has transformed the treatment strategies of several malignancies in the past decades.
Jingyu Zhang, Yu Zhang, Bingxue Qu, Haiyan Yang, Sheng-quan Hu, Xiaowu Dong   +5 more
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‘I will handle it personally’: The neo-patrimonial rhetoric of the Czech Prime Minister in the times of COVID-19

The Journal of Contemporary European Studies, 2021
This paper contributes to the contemporary discussion about the political consequences of the COVID-19 pandemic situation. The goal of the text is to identify and analyze the neo-patrimonial rhetoric of Czech Prime Minister Babiš in connection with his ...
Vladimír Naxera, Ondřej Stulík
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