# [seqfan] Re: New Prime Curio about 199 by Post

Jonathan Post jvospost3 at gmail.com
Tue Sep 15 00:25:56 CEST 2009

```What would be a good way to submit this as a sequence or pair of seqs?

References:
In 1941, Molsen proved that for n equal to or greater than 199, the
interval n < p less than or equal to (8/7)n
always contains a prime of each of the forms 3x+1, 3x-1.

see Zhang, p.3

Generalizations of an Ancient Greek Inequality about the Sequence of Primes
Authors: Shaohua Zhang
(Submitted on 11 Sep 2009 (v1), last revised 12 Sep 2009 (this version, v2))
Abstract: In this note, we generalize an ancient Greek inequality
about the sequence of primes to the cases of arithmetic progressions
even multivariable polynomials with integral coefficients. We also
refine Bouniakowsky's conjecture...

K.Molsen, Zur Verallgemeinerung der Bertrandschen Postulates. Deutsche
Math. 6, 248-256, (1941).

n  floor(8/7)n  #primes 3x-1  #primes 3x+1 (in that interval n < p
less than or equal to (8/7)n)
199   227      1                    2
200   228      1                    2
201   229      1                    3
202   230      1                    3
203   232      1                    3
204   233      2                    3
205   234      2                    3
206   235      2                    3
207   236      2                    3
208   237      2                    3
209   238      2                    3
210   240      3                    3
211   241      3                    4

Primes of form 3x-1 == A003627 = {2, 5, 11, 17, 23, 29, 41, 47, 53,
59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197,
227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359,
383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521,
557, 563, 569, 587, ...}
primes of form 3x+1 == A002476 = {7, 13, 19, 31, 37, 43, 61, 67, 73,
79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223,
229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397,
409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601,
607, 613, 619, ...}

Thank you,

Jonathan Vos Post

```