Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T23:30:03.532579Z
Paper Citation Record · LEDGER
On the arithmetic average of the first $n$ primes
As of 20 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2505.04951.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:14:30.693244Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T16:14:32.789554Z
Reference resolution
14 of 14 outbound references displayed
- verified exact4
- verified fuzzy4
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5bdc4f73-affb-4955-8a1e-a2f6a709baa7 · outbound
This paper cites Sum of primes ≤ n.
On the arithmetic average of the first $n$ primes Sum of primes ≤ n
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T23:30:03.790825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 06e1c439-e8e8-4b5f-87cc-4d67f4c59b3b · outbound
This paper cites Autour de la fonction qui compte le nombre de nombres premiers.
On the arithmetic average of the first $n$ primes Autour de la fonction qui compte le nombre de nombres premiers
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T23:30:03.781290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1b264493-c509-4699-806d-27f66ae7ad4e · outbound
This paper cites A Remark on the Mandl's Inequality.
On the arithmetic average of the first $n$ primes A Remark on the Mandl's Inequality
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T23:30:03.751059Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 38e21fb9-cd54-494f-9f06-cf9662a38c2e · outbound
This paper cites On the asymptotic expansion of the sum of the first n primes.
On the arithmetic average of the first $n$ primes On the asymptotic expansion of the sum of the first n primes
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T23:30:03.738382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9cff0322-835d-4541-953f-a55013b7f401 · outbound
This paper cites On the sum of the first n prime numbers.
On the arithmetic average of the first $n$ primes On the sum of the first n prime numbers
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T23:30:03.725804Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0171cce4-a1f2-45d4-ac1f-e1dfdb5abf60 · outbound
This paper cites New bounds for the sum of the first $n$ prime numbers.
On the arithmetic average of the first $n$ primes New bounds for the sum of the first $n$ prime numbers
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.500934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad1b3c02-4f15-43e2-8573-634d36b88dd4 · outbound
This paper cites On the sum and the average of the first primes.
On the arithmetic average of the first $n$ primes On the sum and the average of the first primes
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T23:30:03.771338Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9690f455-fa64-4dca-a475-b7abdd30fa82 · outbound
This paper cites Numbers m such that the average of the prime numbers up to m is greater than or equal to m/2.
On the arithmetic average of the first $n$ primes Numbers m such that the average of the prime numbers up to m is greater than or equal to m/2
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T23:30:03.761430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2cdc8fb0-5135-48b5-b98e-c9558b698861 · outbound
This paper cites On a sequence involving sums of primes.
On the arithmetic average of the first $n$ primes On a sequence involving sums of primes
Reference 9
- Resolution
- verified exact
- doi, observed 2026-08-15T23:30:03.577003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 531de723-4bb9-4412-846c-66052a3db574 · outbound
This paper cites The n-th Prime is Greater than n log n.
On the arithmetic average of the first $n$ primes The n-th Prime is Greater than n log n
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.518176Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 447a6c54-73c8-4346-a254-cd40b82af59b · outbound
This paper cites Approximate formulas for some functions of prime numbers.
On the arithmetic average of the first $n$ primes Approximate formulas for some functions of prime numbers
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.521539Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e881d08d-4e4d-4f88-97ca-830accf55b9d · outbound
This paper cites Explicit estimates of some functions over primes.
On the arithmetic average of the first $n$ primes Explicit estimates of some functions over primes
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.524923Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a0780dc7-f351-47b8-beec-22a5f5c3c70f · outbound
This paper cites Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap.
On the arithmetic average of the first $n$ primes Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.528893Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 03bbdb33-78b1-46aa-b868-f2d885317d38 · outbound
This paper cites Strong Version of Andrica’s Conjecture.
On the arithmetic average of the first $n$ primes Strong Version of Andrica’s Conjecture
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T23:30:03.532579Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 666e2904-0641-4f17-ad68-a3334d0d1ca5 · inbound
Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ cites this paper.
Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ On the arithmetic average of the first $n$ primes
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:14:32.795081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.