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   https://doi.org/10.1109/LSP.2025.3593178  

   Xia, Xiang-Gen; Guo, Guangpu (January 2025, IEEE Signal Processing Letters)
2. Prime and Thickened Prime Components in Apollonian Circle Packings

   https://doi.org/10.1007/978-3-032-11183-8_8  

   Friedlander, Holley; Fuchs, Elena; Harris, Piper; Hsu, Catherine; Rickards, James; Sanden, Katherine; Schindler, Damaris; Stange, Katherine E (June 2026, Springer Nature Switzerland)

   Abstract Inspired by a question of Sarnak, we introduce the notion of aprime componentin an Apollonian circle packing: a maximal tangency-connected subset having all prime curvatures. We also considerthickened prime components, which are augmented by all circles immediately tangent to the prime component. In both cases, we ask about the curvatures which appear. We consider the residue classes attained by the set of curvatures, the number of circles in such components, the number of distinct integers occurring as curvatures and the number of prime components in a packing. As part of our investigation, we computed and analysed example components up to around curvature$$10^{13}$$ ${10}^{13}$ ; software is available. 

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   Abstract We present the description of the instruments and the first results of the PRime-focus Infrared Microlensing Experiment (PRIME). PRIME is the first dedicated near-infrared (NIR) microlensing survey telescope, and is located at the South African Astronomical Observatory in Sutherland, South Africa. Among its class, it offers one of the widest fields of view in the NIR regime. PRIME’s main goals are (1) to study planetary formation by measuring the frequency and mass function of planets. In particular, we compare results from the central Galactic bulge (GB), accessible only in the NIR by PRIME, with those from the outer GB by optical surveys. (2) To conduct concurrent observations with NASA’s Nancy Grace Roman Space Telescope. Due to the different lines of sight between the ground and space, we detect slight variations in light curves, known as “space-based parallax.” This effect allows us to measure the mass of lens systems and their distance from the Earth. It is the only method to measure the mass of free-floating planets down to Earth mass. We began the GB survey in 2024 February and analyzed images through 2025 June 1, identifying 486 microlensing candidates and over a thousand variable stars, including Mira variables, which are useful for studying the Galactic structure. We issue real-time alerts for follow-up observations, supporting exoplanet searches and the chemical evolution studies in the GB. During the off-bulge season, we conduct an all-sky grid survey and target-of-opportunity observations of transients, including gravitational-wave events,γ-ray bursts, and other science. 

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4. Prime Running Functions

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   Kim, Jaeyoon (October 2020, Experimental Mathematics)

   null (Ed.)
5. On Weakly Prime Modules

   https://doi.org/10.5281/zenodo.18362640  

   Tsutsui, Hisaya (January 2026, Zenodo)