A070248 -id:A070248 - cp's OEIS frontend

A070247 Palindromic primes with digit sum 5.

5, 131, 10301, 1003001, 100030001, 100111001, 101000010000101, 10000010101000001, 101000000010000000101, 110000000010000000011, 10000000000300000000001, 10000100000100000100001, 100000100000010000001000001, 10000000000000300000000000001, 10000000001000100010000000001

Offset: 1

Amarnath Murthy, May 05 2002

It is conjectured that are just 3 palindromic primes with digit sum 2, namely 2, 11 and 101. If any others exist, they must be of the form 10^(2^k) + 1 with k > 14.
From Jeppe Stig Nielsen, Aug 30 2025: (Start)
It is now known that any additional primes 10^(2^k) + 1 must have k >= 31.
Digit sum 3 yields only one prime, 3, a palindrome in a vacuous way.
Digit sum 4 leads to primes (A062339), but such numbers can never be palindromes. Proof: Let w be any palindrome with digit sum 4. So w = 10^a + 10^b + 10^c + 10^d with a >= b >= c >= d >= 0. But then 10^c + 10^d is a nontrivial divisor of w, showing that w is not prime.
You may have come here searching for the subsequence 5, 131, 10301, 1003001, 100030001, 10000000000300000000001, ... where the largest digit exceeds 1. See A171376 and A100028 for information on them.
(End)

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..386 (all terms below 10^1000; terms n = 1..238 from Chai Wah Wu)
Hans Riesel, Some factors of the numbers Gn = 6^2^n+1 and Hn = 10^2^n+1, Math. Comp. 23 (1969), p. 413-415. With errata reported in Math. Comp. 24 (1970), p. 243.

Cf. A002385, A062341, A070248, A070249.

Do[p = Join[ IntegerDigits[n, 4], Reverse[ Drop[ IntegerDigits[n, 4], -1]]]; q = Plus @@ p; If[q == 5 && PrimeQ[ FromDigits[p]] && q == 5, Print[ FromDigits[p]]], {n, 1, 4 10^8}] (* this coding will not pick up the first entry *)

for(i=0,50,for(j=0,i,p=10^(2*i)+10^(i+j)+10^i+10^(i-j)+1;isprime(p)&&print1(p,", "))) \\ Jeppe Stig Nielsen, Aug 30 2025

Edited by Robert G. Wilson v, May 15 2002

More terms from Chai Wah Wu, Nov 25 2015

A070249 Palindromic primes with digit sum 8.

Original entry on oeis.org

10601, 11411, 30203, 31013, 1022201, 1120211, 1300031, 3002003, 100060001, 103000301, 111020111, 300020003, 300101003, 10002220001, 10200200201, 10210001201, 1000030300001, 1021000001201, 1030000000301, 1101010101011

Offset: 1

Amarnath Murthy, May 05 2002

Chai Wah Wu, Table of n, a(n) for n = 1..1757

Cf. A002385, A070247 and A070248.

Do[p = Join[ IntegerDigits[n], Reverse[ Drop[ IntegerDigits[n], -1]]]; q = Plus @@ p; If[ PrimeQ[ FromDigits[p]] && q == 8, Print[ FromDigits[p]]], {n, 1, 10^7}]
Select[Prime[Range[1626*10^4]],Total[IntegerDigits[#]]==8&&PalindromeQ[#]&] (* The program generates the first 13 terms of the sequence. *) (* Harvey P. Dale, Jul 18 2022 *)

Edited by Robert G. Wilson v, May 15 2002

A070250 Palindromic primes with digit sum 10.

Original entry on oeis.org

181, 12421, 30403, 1008001, 1114111, 1212121, 100161001, 100404001, 101060101, 101141101, 102040201, 102202201, 104000401, 130020031, 140000041, 10001610001, 10013031001, 10100600101, 10102220101, 10130003101

Offset: 1

Amarnath Murthy, May 05 2002

Chai Wah Wu, Table of n, a(n) for n = 1..1777

Cf. A002385, A070247, A070248, A070249.

Do[p = IntegerDigits[ Prime[n]]; If[ Plus @@ p == 10 && Reverse[p] == p, Print[ Prime[n]]], {n, 1, 10^10}]
Select[Prime[Range[4607*10^5]],PalindromeQ[#]&&Total[IntegerDigits[#]]==10&] (* Harvey P. Dale, May 28 2023 *)

Edited and extended by Robert G. Wilson v and Jason Earls, May 06 2002

A070831 Palindromic primes with digit sum = 11.

Original entry on oeis.org

191, 353, 13331, 1123211, 1221221, 1303031, 1311131, 3103013, 110232011, 111050111, 112030211, 112111211, 121111121, 130030031, 301111103, 10000900001, 10002520001, 10013131001, 10111311101, 10301110301

Offset: 1

Robert G. Wilson v, May 15 2002

Conjecture: The sequence is unbounded.

Chai Wah Wu, Table of n, a(n) for n = 1..2388

Cf. A002385, A070247, A070248 and A070249.

Do[p = Join[ IntegerDigits[n], Reverse[ Drop[ IntegerDigits[n], -1]]]; q = Plus @@ p; If[ PrimeQ[ FromDigits[p]] && q == 11, Print[ FromDigits[p]]], {n, 1, 10^6}]

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A070247 Palindromic primes with digit sum 5.

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A070249 Palindromic primes with digit sum 8.

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A070250 Palindromic primes with digit sum 10.

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A070831 Palindromic primes with digit sum = 11.

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