Cyclo: search for primes of the form

Φ_3·2ⁿ(b)  =  Φ₆(b²ⁿ⁻¹)  =  Φ₃(−b²ⁿ⁻¹)  =  b²ⁿ − b²ⁿ⁻¹ + 1

Yves Gallot

These generalized unique primes were investigated by P.I.E.S. more than ten years ago.

The smallest base values yielding these primes are OEIS 246119.

Ryan Propper and Serge Batalov found the largest known prime of this form:

- 123447^1048576 − 123447⁵²⁴²⁸⁸ + 1      (5,338,805 digits).

The source code of Cyclo is available on GitHub.

21 Jan 2023: CycloCPU-23.01.0.zip, CPU applications running on Windows or Linux x64.

25 Aug 2017: CycloCPU-2.0.0-src.zip, CPU application running on Microsoft Windows XP x64 or later and a 64-bit x86-compatible CPU.

Jul/Aug 2017: CycloDoc.zip, Documentation and sample source codes (radix-2, radix-4 and radix-4 with 256-bit vectors).

12 Jun 2015: Cyclo-1.1.3.zip  Cyclo-1.1.3-src.zip, Application (CPU or OpenCL) running on Microsoft Windows XP or later and a 32-bit or 64-bit x86-compatible CPU.

27 Apr 2015: CycloCPU-1.0.3.zip  CycloCPU-1.0.3-src.zip, CPU application running on Microsoft Windows XP x64 or later and a 64-bit x86-compatible CPU.

20 Apr 2015: CycloCPU-1.0.2.zip  CycloCPU-1.0.2-src.zip, CPU application running on Microsoft Windows XP x64 or later and a 64-bit x86-compatible CPU.

14 Apr 2015: CycloCPU-1.0.1.zip  CycloCPU-1.0.1-src.zip, CPU application running on Microsoft Windows XP x64 or later and a 64-bit x86-compatible CPU with Advanced Vector Extensions.

31 Jan 2015: CycloOCL-1.0.1.zip  CycloOCL-1.0.1-src.zip, OpenCL application running on Microsoft Windows XP or later and a 32-bit or 64-bit x86-compatible CPU.

8 Jan 2015: CycloOCL-0.2.zip  CycloOCL-0.2-src.zip, OpenCL application running on Microsoft Windows XP or later and a 32-bit or 64-bit x86-compatible CPU.

27 Dec 2014: CycloOCL-0.1.zip  CycloOCL-0.1-src.zip, OpenCL application running on Microsoft Windows XP or later and a 32-bit or 64-bit x86-compatible CPU.

Copyright (C) 2014-2023, Yves Gallot.
All rights reserved.