A204189 -id:A204189 - cp's OEIS frontend

A002110 Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.

1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070, 117288381359406970983270, 7858321551080267055879090

Offset: 0

N. J. A. Sloane and J. H. Conway

See A034386 for the second definition of primorial numbers: product of primes in the range 2 to n.
a(n) is the least number N with n distinct prime factors (i.e., omega(N) = n, cf. A001221). - Lekraj Beedassy, Feb 15 2002
Phi(n)/n is a new minimum for each primorial. - Robert G. Wilson v, Jan 10 2004
Smallest number stroked off n times after the n-th sifting process in an Eratosthenes sieve. - Lekraj Beedassy, Mar 31 2005
Apparently each term is a new minimum for phi(x)*sigma(x)/x^2. 6/Pi^2 < sigma(x)*phi(x)/x^2 < 1 for n > 1. - Jud McCranie, Jun 11 2005
Let f be a multiplicative function with f(p) > f(p^k) > 1 (p prime, k > 1), f(p) > f(q) > 1 (p, q prime, p < q). Then the record maxima of f occur at n# for n >= 1. Similarly, if 0 < f(p) < f(p^k) < 1 (p prime, k > 1), 0 < f(p) < f(q) < 1 (p, q prime, p < q), then the record minima of f occur at n# for n >= 1. - David W. Wilson, Oct 23 2006
Wolfe and Hirshberg give ?, ?, ?, ?, ?, 30030, ?, ... as a puzzle.
Records in number of distinct prime divisors. - Artur Jasinski, Apr 06 2008
For n >= 2, the digital roots of a(n) are multiples of 3. - Parthasarathy Nambi, Aug 19 2009 [with corrections by Zak Seidov, Aug 30 2015]
Denominators of the sum of the ratios of consecutive primes (see A094661). - Vladimir Joseph Stephan Orlovsky, Oct 24 2009
Where record values occur in A001221. - Melinda Trang (mewithlinda(AT)yahoo.com), Apr 15 2010
It can be proved that there are at least T prime numbers less than N, where the recursive function T is: T = N - N*Sum_{i = 0..T(sqrt(N))} A005867(i)/A002110(i). This can show for example that at least 0.16*N numbers are primes less than N for 29^2 > N > 23^2. - Ben Paul Thurston, Aug 23 2010
The above comment from Parthasarathy Nambi follows from the observation that digit summing produces a congruent number mod 9, so the digital root of any multiple of 3 is a multiple of 3. prime(n)# is divisible by 3 for n >= 2. - Christian Schulz, Oct 30 2013
The peaks (i.e., local maximums) in a graph of the number of repetitions (i.e., the tally of values) vs. value, as generated by taking the differences of all distinct pairs of odd prime numbers within a contiguous range occur at regular periodic intervals given by the primorial numbers 6 and greater. Larger primorials yield larger (relative) peaks, however the range must be >50% larger than the primorial to be easily observed. Secondary peaks occur at intervals of those "near-primorials" divisible by 6 (e.g., 42). See A259629. Also, periodicity at intervals of 6 and 30 can be observed in the local peaks of all possible sums of two, three or more distinct odd primes within modest contiguous ranges starting from p(2) = 3. - Richard R. Forberg, Jul 01 2015
If a number k and a(n) are coprime and k < (prime(n+1))^b < a(n), where b is an integer, then k has fewer than b prime factors, counting multiplicity (i.e., bigomega(k) < b, cf. A001222). - Isaac Saffold, Dec 03 2017
If n > 0, then a(n) has 2^n unitary divisors (A034444), and a(n) is a record; i.e., if k < a(n) then k has fewer unitary divisors than a(n) has. - Clark Kimberling, Jun 26 2018
Unitary superabundant numbers: numbers k with a record value of the unitary abundancy index, A034448(k)/k > A034448(m)/m for all m < k. - Amiram Eldar, Apr 20 2019
Psi(n)/n is a new maximum for each primorial (psi = A001615) [proof in link: Patrick Sole and Michel Planat, proposition 1 page 2]; compare with comment 2004: Phi(n)/n is a new minimum for each primorial. - Bernard Schott, May 21 2020
The term "primorial" was coined by Harvey Dubner (1987). - Amiram Eldar, Apr 16 2021
a(n)^(1/n) is approximately (n log n)/e. - Charles R Greathouse IV, Jan 03 2023
Subsequence of A267124. - Frank M Jackson, Apr 14 2023

			a(9) = 23# = 2*3*5*7*11*13*17*19*23 = 223092870 divides the difference 5283234035979900 in the arithmetic progression of 26 primes A204189. - _Jonathan Sondow_, Jan 15 2012

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 50.
G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 49.
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 4.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 114.
D. Wolfe and S. Hirshberg, Underspecified puzzles, in Tribute to A Mathemagician, Peters, 2005, pp. 73-74.

Alex Ermolaev, Table of n, a(n) for n = 0..350 (terms up to a(100) from T. D. Noe)
Iskander Aliev, Jesús De Loera, Fritz Eisenbrand, Timm Oertel, and Robert Weismantel, The Support of Integer Optimal Solutions, arXiv:1712.08923 [math.OC], 2017.
C. K. Caldwell, The Prime Glossary, Primorial.
Geoffrey Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, arXiv:1112.6010 [math.NT], 2011-2012; Ramanujan J., 29 (2012), 359-384.
Harvey Dubner, Factorial and primorial primes, J. Rec. Math., Vol. 19, No. 3 (1987), pp. 197-203. (Annotated scanned copy)
F. Ellermann, Illustration for A002110, A005867, A038110, A060753.
S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 209-210.
D. J. Greenhoe, MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing, 2014.
Daniel J. Greenhoe, Frames and Bases: Structure and Design, Version 0.20, Signal Processing ABCs series (2019) Vol. 4, pp. 7, 81.
Daniel J. Greenhoe, A Book Concerning Transforms, Version 0.10, Signal Processing ABCs series (2019) Vol. 5, see page 7.
A. W. Lin and S. Zhou, A linear-time algorithm for the orbit problem over cyclic groups, preprint, CONCUR 2014 - Concurrency Theory, Volume 8704 of the series Lecture Notes in Computer Science pp. 327-341.
A. W. Lin and S. Zhou, A linear-time algorithm for the orbit problem over cyclic groups, CONCUR 2014 - Concurrency Theory, Lecture Notes in Computer Science, Volume 8704, 2014, pp. 327-341.
F. E. Masat, Letter to N. J. A. Sloane with attachment: "A note on prime number sequences" (unpublished manuscript), Apr. 1991.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv:1202.3670 [math.HO], 2012.
Thomas Morrill, Further Development of "Non-Pythagorean" Musical Scales Based on Logarithms, arXiv:1804.08067 [math.HO], 2018.
J.-L. Nicolas, Petites valeurs de la fonction d'Euler, J. Number Theory 17, no.3 (1983), 375-388.
Patrick Sole and Michel Planat, The Robin inequality for 7-free integers, INTEGERS, 2011, #A65.
Andrew V. Sutherland, Order Computations in Generic Groups, Ph. D. Dissertation, Math. Dept., M.I.T., 2007.
G. Villemin's Almanach of Numbers, Primorielle.
Eric Weisstein's World of Mathematics, Primorial.
Robert G. Wilson v, Letter to N. J. A. Sloane, Jan. 1994.
Index to divisibility sequences
Index entries for "core" sequences
Index entries for sequences related to primorial base
Index entries for sequences related to primorial numbers

A034386 gives the second version of the primorial numbers.
Subsequence of A005117 and of A064807. Apart from the first term, a subsequence of A083207.
Cf. A001615, A002182, A002201, A003418, A005235, A006862, A034444 (unitary divisors), A034448, A034387, A033188, A035345, A035346, A036691 (compositorial numbers), A049345 (primorial base representation), A057588, A060735 (and integer multiples), A061742 (squares), A072938, A079266, A087315, A094348, A106037, A121572, A053589, A064648, A132120, A260188.
Cf. A061720 (first differences), A143293 (partial sums).
Cf. also A276085, A276086.
The following fractions are all related to each other: Sum 1/n: A001008/A002805, Sum 1/prime(n): A024451/A002110 and A106830/A034386, Sum 1/nonprime(n): A282511/A282512, Sum 1/composite(n): A250133/A296358.

a002110 n = product $ take n a000040_list
a002110_list = scanl (*) 1 a000040_list
-- Reinhard Zumkeller, Feb 19 2012, May 03 2011

[1] cat [&*[NthPrime(i): i in [1..n]]: n in [1..20]]; // Bruno Berselli, Oct 24 2012

[1] cat [&*PrimesUpTo(p): p in PrimesUpTo(60)]; // Bruno Berselli, Feb 08 2015

A002110 := n -> mul(ithprime(i),i=1..n);

FoldList[Times, 1, Prime[Range[20]]]
primorial[n_] := Product[Prime[i], {i, n}]; Array[primorial,20] (* José María Grau Ribas, Feb 15 2010 *)
Join[{1}, Denominator[Accumulate[1/Prime[Range[20]]]]] (* Harvey P. Dale, Apr 11 2012 *)

a(n)=prod(i=1,n, prime(i)) \\ Washington Bomfim, Sep 23 2008

p=1; for (n=0, 100, if (n, p*=prime(n)); write("b002110.txt", n, " ", p) )  \\ Harry J. Smith, Nov 13 2009

a(n) = factorback(primes(n)) \\ David A. Corneth, May 06 2018

from sympy import primorial
def a(n): return 1 if n < 1 else primorial(n)
[a(n) for n in range(51)]  # Indranil Ghosh, Mar 29 2017

[sloane.A002110(n) for n in (1..20)] # Giuseppe Coppoletta, Dec 05 2014

; with memoization-macro definec
(definec (A002110 n) (if (zero? n) 1 (* (A000040 n) (A002110 (- n 1))))) ;; Antti Karttunen, Aug 30 2016

Asymptotic expression for a(n): exp((1 + o(1)) * n * log(n)) where o(1) is the "little o" notation. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 08 2001
a(n) = A054842(A002275(n)).
Binomial transform = A136104: (1, 3, 11, 55, 375, 3731, ...). Equals binomial transform of A121572: (1, 1, 3, 17, 119, 1509, ...). - Gary W. Adamson, Dec 14 2007
a(0) = 1, a(n+1) = prime(n)*a(n). - Juri-Stepan Gerasimov, Oct 15 2010
a(n) = Product_{i=1..n} A000040(i). - Jonathan Vos Post, Jul 17 2008
a(A051838(n)) = A116536(n) * A007504(A051838(n)). - Reinhard Zumkeller, Oct 03 2011
A000005(a(n)) = 2^n. - Carlos Eduardo Olivieri, Jun 16 2015
a(n) = A035345(n) - A005235(n) for n > 0. - Jonathan Sondow, Dec 02 2015
For all n >= 0, a(n) = A276085(A000040(n+1)), a(n+1) = A276086(A143293(n)). - Antti Karttunen, Aug 30 2016
A054841(a(n)) = A002275(n). - Michael De Vlieger, Aug 31 2016
a(n) = A270592(2*n+2) - A270592(2*n+1) if 0 <= n <= 4 (conjectured for all n by Alon Kellner). - Jonathan Sondow, Mar 25 2018
Sum_{n>=1} 1/a(n) = A064648. - Amiram Eldar, Oct 16 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = A132120. - Amiram Eldar, Apr 12 2021
Theta being Chebyshev's theta function, a(0) = exp(theta(1)), and for n > 0, a(n) = exp(theta(m)) for A000040(n) <= m < A000040(n+1) where m is an integer. - Miles Englezou, Nov 26 2024

A033188 Minimal difference of any increasing arithmetic progression of n primes.

Original entry on oeis.org

0, 1, 2, 6, 6, 30, 150, 210, 210, 210, 2310, 2310, 30030, 30030, 30030, 30030, 510510, 510510, 9699690, 9699690, 9699690

Offset: 1

Eric W. Weisstein

The entries shown have been proved to be correct.

Jens Kruse Andersen, Status of minimal arithmetic progressions of primes
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Index entries for sequences related to primes in arithmetic progressions

Cf. A033189 (initial terms), A113872 (last terms).

Cf. A034386, A204189.

David W. Wilson conjectures that a(n) = n# (n primorial, A034386) for n >= 8. If this is true then a(22) onwards are: 9699690, 223092870, 223092870, 223092870, 223092870, 223092870, 223092870, 6469693230, 6469693230, ...

Entry revised Feb 02 2006 by N. J. A. Sloane, based on suggestions from Jens Kruse Andersen.

A260751 25 primes in arithmetic progression: a(n) = 6171054912832631 + (n-1)*81737658082080 for n = 1, 2, ..., 25.

Original entry on oeis.org

6171054912832631, 6252792570914711, 6334530228996791, 6416267887078871, 6498005545160951, 6579743203243031, 6661480861325111, 6743218519407191, 6824956177489271, 6906693835571351, 6988431493653431, 7070169151735511, 7151906809817591, 7233644467899671

Offset: 1

Marco Ripà, Aug 05 2015

This was the longest known sequence of primes in arithmetic progression from 17 May 2008 to 12 April 2010.

			a(25) = 6171054912832631 + 24*81737658082080 = 8132758706802551 is prime.

Marco Ripà, Table of n, a(n) for n = 1..25
Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.

Cf. A002110, A204189, A261140, A327760, A363980, A374949.

[6171054912832631+(n-1)*81737658082080: n in [1..25]]; // Bruno Berselli, Aug 06 2015

Table[6171054912832631 + (n - 1) 81737658082080, {n, 1, 25}] (* Bruno Berselli, Aug 06 2015 *)

[6171054912832631+(n-1)*81737658082080 for n in (1..25)] # Bruno Berselli, Aug 06 2015

a(n) = 6171054912832631 + (n-1)*366384*A002110(9) with 1 <= n <= 25.

A261140 a(n) = 3486107472997423 + (n-1)*371891575525470.

Original entry on oeis.org

3486107472997423, 3857999048522893, 4229890624048363, 4601782199573833, 4973673775099303, 5345565350624773, 5717456926150243, 6089348501675713, 6461240077201183, 6833131652726653, 7205023228252123, 7576914803777593, 7948806379303063, 8320697954828533

Offset: 1

Marco Ripà, Aug 10 2015

The terms n = 1..26 are prime. This is the longest sequence of primes in arithmetic progression with smallest end, a(26)=12783396861134173, known as of August 10, 2015.

			a(26) = 3486107472997423 + 25*371891575525470 = 12783396861134173 is prime.

Colin Barker, Table of n, a(n) for n = 1..1000
Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A002110, A033188, A033290, A204189, A260751, A327760, A363980, A374949.

[3486107472997423+(n-1)*371891575525470: n in [1..20]];

Table[3486107472997423 + (n - 1) 371891575525470, {n, 1, 20}]
LinearRecurrence[{2,-1},{3486107472997423,3857999048522893},20] (* Harvey P. Dale, May 14 2022 *)

Vec(-x*(3114215897471953*x-3486107472997423)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

a(n) = 3486107472997423 + (n-1)*1666981*A002110(9).

G.f.: -x*(3114215897471953*x-3486107472997423) / (x-1)^2. - Colin Barker, Aug 25 2015

A033290 Ten consecutive primes in arithmetic progression.

Original entry on oeis.org

100996972469714247637786655587969840329509324689190041803603417758904341703348882159067229719, 100996972469714247637786655587969840329509324689190041803603417758904341703348882159067229929, 100996972469714247637786655587969840329509324689190041803603417758904341703348882159067230139

Offset: 0

Manfred Toplic

This was the first known case, found in 1998. The full 10 terms are linked below. - Jens Kruse Andersen, Jun 30 2014

Jens Kruse Andersen, Table of n, a(n) for n = 0..9
J. K. Andersen, The largest known CPAP-10
H. Dubner et al., Ten consecutive primes in arithmetic progression
T. Forbes, Ten consecutive primes in arithmetic progression
Tanya Khovanova, Non Recursions
Manfred Toplic, Nine and ten primes project
Eric Weisstein's World of Mathematics, Primes in Arithmetic Progression
Index entries for sequences related to primes in arithmetic progressions

Cf. A033188, A204189, A260751, A261140, A327760, A363980, A374949.

N*m + x + 210*b, b = 0..9.

a(n) = a(0)+210*n, and a(n+1) = nextprime(a(n)+1). - Jens Kruse Andersen, Jun 30 2014

A327760 Primes in Rob Gahan's arithmetic progression of 27 primes.

Original entry on oeis.org

224584605939537911, 242720302537486841, 260855999135435771, 278991695733384701, 297127392331333631, 315263088929282561, 333398785527231491, 351534482125180421, 369670178723129351, 387805875321078281, 405941571919027211, 424077268516976141, 442212965114925071

Offset: 1

Felix Fröhlich, Sep 25 2019

This arithmetic progression of 27 primes (AP27) was discovered by Rob Gahan on 23 September 2019 as part of PrimeGrid's AP27 Search subproject (cf. Goetz, 2019).

Felix Fröhlich, Table of n, a(n) for n = 1..27
M. Goetz, World's First AP27!!!, PrimeGrid forum, Sep 23, 2019.
PrimeGrid, 224584605939537911+81292139*23#*n for n=0..26
PrimeGrid, Official announcement of the AP27
Stéphane Vinatier and William Reginald Alcorn, Mathematics as seen by an artist: Inspiring mathematical objects, Eur. Math. Soc. Mag. (2025) Vol. 135, 20-31. See p. 26.
Index entries for sequences related to primes in arithmetic progressions

Cf. A033188, A033290, A204189, A260751, A261140, A363980, A374949.

A327760[n_] := 224584605939537911 + (n-1)*18135696597948930;
Array[A327760, 27] (* Paolo Xausa, Jan 30 2024 *)

vector(27, t, 224584605939537911+81292139*223092870*(t-1))

A363980 Tom Greer's arithmetic progression of 27 primes.

Original entry on oeis.org

277699295941594831, 315809464967513821, 353919633993432811, 392029803019351801, 430139972045270791, 468250141071189781, 506360310097108771, 544470479123027761, 582580648148946751, 620690817174865741, 658800986200784731, 696911155226703721, 735021324252622711

Offset: 1

Marco Ripà, Jun 30 2023

At the time of submission (June 2023), this sequence is the arithmetic progression of 27 primes having the largest known initial and final term and it was found by Tom Greer on 26 May 2023 as part of PrimeGrid's AP27, running the program AP26 (this is the second known AP27 to date, see A327760).

			a(3) = 277699295941594831 + 2*170826477*223092870 is prime.

Marco Ripà, Table of n, a(n) for n = 1..27
PrimeGrid, Official announcement of the second known AP27
PrimeGrid forum, Message 163220 (World's Second AP27!!!)

Cf. A033188, A033290, A204189, A260751, A261140, A327760, A374949.

A363980[n_]:=277699295941594831 + (n-1)*38110169025918990;
Array[A363980, 27] (* Paolo Xausa, Jan 30 2024 *)

vector(27, t, 277699295941594831+170826477*223092870*(t-1))

a(n+1) = 277699295941594831 + n*170826477*223092870, for n = 0, 1, ..., 26.

A374949 Michael Kwok's arithmetic progression of 27 primes.

Original entry on oeis.org

605185576317848261, 639847242910261121, 674508909502673981, 709170576095086841, 743832242687499701, 778493909279912561, 813155575872325421, 847817242464738281, 882478909057151141, 917140575649564001, 951802242241976861, 986463908834389721, 1021125575426802581

Offset: 1

Marco Ripà, Jul 24 2024

At the time of submission (July 2024), this sequence is the arithmetic progression of 27 primes having the largest known initial and final term and it was found by Michael Kwok on 10 December 2023 as part of the project PrimeGrid, running the program AP26 (this is the third known AP27 to date, see A327760 and A363980).

			a(3) = 605185576317848261 + 2*34661666592412860 is prime.

PrimeGrid forum, Message 167007 (World's Third AP27!!!).

Cf. A033188, A033290, A204189, A260751, A261140, A327760, A363980.

A374949[n_]:=605185576317848261 + (n-1)* 34661666592412860; Array[A374949, 27]

vector(27, t, 605185576317848261+155368778*223092870*(t-1))

a(n+1) = 605185576317848261 + n*34661666592412860, for n = 0, 1, ..., 26.

A317163 a(n) = 48277590120607451 + (n-1)*8440735245322380.

Original entry on oeis.org

48277590120607451, 56718325365929831, 65159060611252211, 73599795856574591, 82040531101896971, 90481266347219351, 98922001592541731, 107362736837864111, 115803472083186491, 124244207328508871, 132684942573831251, 141125677819153631, 149566413064476011

Offset: 1

Marco Ripà, Jul 23 2018

a(1), a(2), ..., a(26) are prime. As of Jul 23 2018, this is one of the longest known sequences of primes in arithmetic progression, and was found by Bruce E. Slade in 2017.

			a(26) = 48277590120607451 + 25*37835074*223092870 = 259295971253666951 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.

Cf. A002110, A204189, A260751, A261140.

List([1..26],n->55837783597462913+(n-1)*13858932213216090); # Marco Ripà, Aug 10 2018

seq(48277590120607451+(n-1)*8440735245322380,n=1..26); # Marco Ripà, Aug 10 2018

Table[48277590120607451 + (n - 1) 8440735245322380, {n, 1, 26}]

a(n) = 48277590120607451 + a(n-1)*37835074*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.

A317164 a(n) = 55837783597462913 + (n-1)*13858932213216090.

Original entry on oeis.org

55837783597462913, 69696715810679003, 83555648023895093, 97414580237111183, 111273512450327273, 125132444663543363, 138991376876759453, 152850309089975543, 166709241303191633, 180568173516407723, 194427105729623813, 208286037942839903, 222144970156055993

Offset: 1

Marco Ripà, Jul 23 2018

The terms for n = 1..26 are prime. As of Jul 23 2018, this is one of the longest known sequences of primes in arithmetic progression.

			a(26) = 55837783597462913 + 25*62121807*223092870 = 402311088927865163 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.

Cf. A002110, A204189, A260751, A261140, A317163.

List([1..25],n->55837783597462913+(n-1)*13858932213216090); # Muniru A Asiru, Jul 24 2018

seq(55837783597462913+(n-1)*13858932213216090,n=1..15); # Muniru A Asiru, Jul 24 2018

Table[55837783597462913 + (n - 1) 13858932213216090, {n, 1, 25}]

a(n) = 455837783597462913 + a(n-1)*62121807*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.

cp's OEIS Frontend

A002110 Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.

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A033188 Minimal difference of any increasing arithmetic progression of n primes.

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A260751 25 primes in arithmetic progression: a(n) = 6171054912832631 + (n-1)*81737658082080 for n = 1, 2, ..., 25.

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A261140 a(n) = 3486107472997423 + (n-1)*371891575525470.

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A033290 Ten consecutive primes in arithmetic progression.

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A327760 Primes in Rob Gahan's arithmetic progression of 27 primes.

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A363980 Tom Greer's arithmetic progression of 27 primes.

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