A033168 Longest arithmetic progression of primes with difference 210 and minimal initial term.

199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089

Offset: 0

Author

Manuel Valdivia, Apr 22 1998

Keywords

• nonn
• fini
• full

Comments

Since 210 == 1 (mod 11), a progression of primes with difference 210 can't have more than ten terms because there is exactly one multiple of 11 within each run of eleven consecutive terms. For example, 2089 + 210 = 2299 = 11^2 * 19. - Alonso del Arte, Dec 22 2017, edited by M. F. Hasler, Jan 02 2020

After 199, the next prime which starts a CPAP-10 with common gap 210 is 243051733. See A094220 for further starting points. - M. F. Hasler, Jan 02 2020

References

• Paul Glendinning, Math in Minutes: 200 Key Concepts Explained in an Instant. New York, London: Quercus (2013): pp. 316-317.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 143.

Links

• Tanya Khovanova, Non Recursions.
• OEIS wiki, Primes in arithmetic progression.
• Index entries for sequences related to primes in arithmetic progressions.

Crossrefs

Row 10 of A086786, A113470, A133276, A133277.

Cf. A094220.

Programs

Mathematica

199 + 210*Range[0, 9] (* Paolo Xausa, Sep 14 2024 *)

PARI

forprime(p=1,,for(i=1,9,isprime(p+i*210)||next(2)); return([p+d|d<-[0..9]*210])) \\ M. F. Hasler, Jan 02 2020

Formula

a(n) = a(0) + n*210 for 0 <= n <= 9. - M. F. Hasler, Jan 02 2020