A342443 a(n) is the largest prime < 10^n that is the sum of at least two consecutive primes.

5, 97, 991, 9949, 99971, 999983, 9999991, 99999989, 999999937, 9999999943, 99999999977, 999999999989, 9999999999763, 99999999999959, 999999999999989

Offset: 1

Author

Bernard Schott, Mar 12 2021

Keywords

• nonn
• base
• more

Comments

The minimum corresponding number of consecutive primes to get this largest prime a(n) is A342444(n) and the first prime of these A342444(n) consecutive primes is A342454(n).

Differs from A342439 where the corresponding primes result of the longest sum < 10^n of consecutive primes.

a(n) is the largest n-digit prime A003618(n) for n = 2, 6, 7, 8, 9, 11, 12, ...

a(13) >= k = 10^13 - 237. If a(13) > k then it is the sum of at least 30000 primes. k can be written as the sum of 6449 consecutive primes. - David A. Corneth, Mar 13 2021

No sum of 30000 or more consecutive primes is in the interval [10^13 - 237, 10^13 - 1], so a(13) = 10^13 - 237. - Jon E. Schoenfield, Mar 14 2021

Examples

			a(1) = 5 = 2 + 3, since it is not possible to obtain the greatest 1-digit prime 7 when adding consecutive primes.
a(2) = 29 + 31 + 37 = 97, since (29, 31, 37) are consecutive primes and 97 is the largest 2-digit prime.
		

Crossrefs

Cf. A003618, A050936, A067377, A342439, A342440, A342444, A342453, A342454.

Formula

A342439(n) <= a(n) <= A003618(n).

Extensions

a(9) from Jinyuan Wang, Mar 13 2021

a(10) from David A. Corneth, Mar 13 2021

a(11)-a(12) from Jinyuan Wang, Mar 13 2021

a(13)-a(14) from Jon E. Schoenfield, Mar 13 2021

a(15) from Max Alekseyev, Dec 11 2024