Paper Citation Record · LEDGER

Prime numbers with an almost prime reverse

As of 19 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2506.21642.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.21642 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:48:08.768483Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:29:26.909653Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-06-30T16:54:58.627966Z

Reference resolution

34 of 34 outbound references displayed

verified exact0
verified fuzzy24
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation af86c899-2d6e-4ce4-b201-5d34355d7dcb · outbound

This paper cites Barat, B.

Prime numbers with an almost prime reverse Barat, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:14.675047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d7383af3-48f3-4f16-af49-6c8b5bdf54d2 · outbound

This paper cites On Telhcirid's theorem on arithmetic progressions.

Prime numbers with an almost prime reverse On Telhcirid's theorem on arithmetic progressions

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:06.344429Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09caa0c5-7c2f-44f6-bbb1-e3cfc5eaf54a · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:14.480187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e5137758-236e-4230-8ef0-9743deef58a9 · outbound

This paper cites Bourgain , Prescribing the binary digits of primes , Israel J.

Prime numbers with an almost prime reverse Bourgain , Prescribing the binary digits of primes , Israel J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:14.255833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b9d83ebc-c55f-4de0-8c2f-9429d4f0db64 · outbound

This paper cites Math., 206 (2015), pp.

Prime numbers with an almost prime reverse Math., 206 (2015), pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:14.048853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 092020fd-4fd5-4adf-a058-257bf4248cc0 · outbound

This paper cites Powerfree integers and Fourier bounds.

Prime numbers with an almost prime reverse Powerfree integers and Fourier bounds

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:06.558367Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69093189-32fe-4a16-b0f5-1a1117502e4d · outbound

This paper cites Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes , Scientia Sinica, 16 (1973), pp.

Prime numbers with an almost prime reverse Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes , Scientia Sinica, 16 (1973), pp

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.824697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bab669a2-9352-4dd9-9059-ce8e121dcd68 · outbound

This paper cites Chourasiya and D.

Prime numbers with an almost prime reverse Chourasiya and D

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:06.677200Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6079b95-11a7-4489-b041-48540b5db316 · outbound

This paper cites Cohen, Number theory.

Prime numbers with an almost prime reverse Cohen, Number theory

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.626293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 891649ac-8876-43fe-8136-9fb690514696 · outbound

This paper cites Col , Palindromes dans les progressions arithm´ etiques, Acta Arith., 137 (2009), pp.

Prime numbers with an almost prime reverse Col , Palindromes dans les progressions arithm´ etiques, Acta Arith., 137 (2009), pp

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.493179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3d750b3c-d598-454b-a149-3d14a7db5d5e · outbound

This paper cites Dartyge, B.

Prime numbers with an almost prime reverse Dartyge, B

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.382682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fcfdce2b-5584-45ea-990e-46a30e824618 · outbound

This paper cites Dartyge and C.

Prime numbers with an almost prime reverse Dartyge and C

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.233042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 421f23ba-c544-435c-a831-5395f655f292 · outbound

This paper cites Number Theory, 91 (2001), pp.

Prime numbers with an almost prime reverse Number Theory, 91 (2001), pp

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:13.097828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d33e555-ea42-45ba-b037-33aa68199aeb · outbound

This paper cites Dartyge and G.

Prime numbers with an almost prime reverse Dartyge and G

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:12.937096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation be347cc9-e4b0-4378-a2b2-20f41d677c68 · outbound

This paper cites London Math.

Prime numbers with an almost prime reverse London Math

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:12.803491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 835ab93c-5390-48b3-beb5-4f1616377c06 · outbound

This paper cites Fouvry and C.

Prime numbers with an almost prime reverse Fouvry and C

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:12.657309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 550ec2b0-ceb5-4354-8b6a-86e7ec99a9a8 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:12.492969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 95567554-feb9-4b47-8fb1-5d14fdf7cbae · outbound

This paper cites Friedlander and H.

Prime numbers with an almost prime reverse Friedlander and H

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:12.129393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7bd31387-c6d0-498d-959e-4397ef7f5c74 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:11.923997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation daa8eb24-c2f5-486c-9d43-0d9f37761a5f · outbound

This paper cites Greaves, Sieves in number theory , vol.

Prime numbers with an almost prime reverse Greaves, Sieves in number theory , vol

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:11.725657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8f0be984-3bac-4505-8324-3f7de412ac56 · outbound

This paper cites Halberstam and H.-R.

Prime numbers with an almost prime reverse Halberstam and H.-R

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:11.610897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f18eaf47-f297-4b3c-a26c-671830df1fea · outbound

This paper cites Iwaniec, Rosser’s sieve, Acta Arith., 36 (1980), pp.

Prime numbers with an almost prime reverse Iwaniec, Rosser’s sieve, Acta Arith., 36 (1980), pp

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:11.495218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0417835b-816f-4b24-9d64-bdc47e133fa0 · outbound

This paper cites Iwaniec and E.

Prime numbers with an almost prime reverse Iwaniec and E

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:11.216161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4639d01c-7539-40f3-b6ae-7c7c56f90b45 · outbound

This paper cites Mauduit and J.

Prime numbers with an almost prime reverse Mauduit and J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:11.075847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0ac9a3be-e4dc-4740-a818-d93fbb74d238 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:10.888128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 97b8199a-03f2-4fff-a685-bb638663c477 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:10.747361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aaba1fc9-db7e-4e0b-abbb-84e68147d10a · outbound

This paper cites Maynard, Primes with restricted digits , Invent.

Prime numbers with an almost prime reverse Maynard, Primes with restricted digits , Invent

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:10.471394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a9e31691-202a-42cb-af21-c1bad1581277 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:10.247447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4f1c1994-45a3-4179-a7d5-845ff0eab3d2 · outbound

This paper cites an unresolved cited work.

Prime numbers with an almost prime reverse Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:10.047135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e987d900-7ebb-4286-a268-137b6059c37c · outbound

This paper cites R´enyi, On the representation of an even number as the sum of a single prime and single almost-prime number , Izv.

Prime numbers with an almost prime reverse R´enyi, On the representation of an even number as the sum of a single prime and single almost-prime number , Izv

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:09.875998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dc5c27aa-d92f-4278-bbab-dd7d007a91b8 · outbound

This paper cites Swaenepoel , Prime numbers with a positive proportion of preassigned digits , Proc.

Prime numbers with an almost prime reverse Swaenepoel , Prime numbers with a positive proportion of preassigned digits , Proc

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:09.756245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fd7a364f-a2c3-4754-8b49-c8ec521cdd39 · outbound

This paper cites Tenenbaum , Introduction ` a la th´ eorie analytique et probabiliste des nombres , Dunod, cinqui` eme ed., 2022.

Prime numbers with an almost prime reverse Tenenbaum , Introduction ` a la th´ eorie analytique et probabiliste des nombres , Dunod, cinqui` eme ed., 2022

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:09.562494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1403a2d8-878b-4cc1-98e7-073815578c26 · outbound

This paper cites Tuxanidy and D.

Prime numbers with an almost prime reverse Tuxanidy and D

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:09.356535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a2473438-fccd-40c6-9244-80ad2dc3b08c · outbound

This paper cites Zygmund , Trigonometric series.

Prime numbers with an almost prime reverse Zygmund , Trigonometric series

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:09.161449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 8b986cfe-d0e6-4395-9b75-fe8c64274ef0 · inbound

The Zsiflaw--Legeis theorem for arbitrary bases cites this paper.

The Zsiflaw--Legeis theorem for arbitrary bases Prime numbers with an almost prime reverse

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T18:29:26.909653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f42f40ff-2a96-4f38-a344-e1e67123d24f · inbound

The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem cites this paper.

The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem Prime numbers with an almost prime reverse

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-22T06:21:10.684987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0470fb5e-5a28-4cf4-aa2c-acd6f4c9ff74 · inbound

The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem cites this paper.

The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem Prime numbers with an almost prime reverse

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-06-30T16:54:58.631818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.