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Prime numbers p such that all prime factors of p+1 and p-1 are smaller than the cube root of p.
1

%I #28 Mar 03 2024 10:15:38

%S 449,4159,4801,4999,8191,11551,11969,15731,16561,22541,26449,28729,

%T 31249,33857,35153,38501,39929,42283,45631,46817,47431,47501,48049,

%U 51679,52021,62929,63799,68449,69191,81919,83231,84967,89909,94771,97499,100049,104059

%N Prime numbers p such that all prime factors of p+1 and p-1 are smaller than the cube root of p.

%H Lei Zhou, <a href="/A283791/b283791.txt">Table of n, a(n) for n = 1..10000</a>

%e 449 is a prime number. 449+1 = 450 = 2*3^2*5^2, 5^3 = 125 < 449; 449-1 = 448 = 2^6*7, 7^3 = 343 < 449, so 449 is in this list.

%e 457 is a prime number. 457+1 = 458 = 2*229, 229^3 > 457, so 457 is NOT in this list.

%t p = 1; Table[

%t While[p = NextPrime[p]; fp = Last[FactorInteger[p + 1]][[1]];

%t fm = Last[FactorInteger[p - 1]][[1]]; (fp^3 >= p) || (fm^3 >=

%t p)]; p, {n, 1, 37}]

%o (PARI) isok(p) = isprime(p) && (p>2) && (vecmax(factor(p-1)[,1])^3 < p) && (vecmax(factor(p+1)[,1])^3 < p); \\ _Michel Marcus_, Jan 10 2018

%Y Cf. A000040.

%K nonn,easy

%O 1,1

%A _Lei Zhou_, Mar 16 2017

%E Definition corrected by _Zak Seidov_, Dec 04 2017