Recreational Mathematics · Prime Numbers

Fixed Digit-Split Repetitions Prime Patterns

Created by Inder J. Taneja

Split a fixed digit block into at least two parts and insert those parts at different positions of a prime seed. Repeat each part at its own position. For example, block 21 split as 2 | 1 with seed 13 gives 13 → 2131 → 221311 → 22213111.

Choose the search

The block is split into consecutive parts, retaining its digit order. Each part goes into a different gap of the seed; gaps can be at the front, between seed digits, or at the end. For 3d–9d, the suggested starting range is 100 blocks. Set the two block limits equal to search one block. A 2d value 7 is treated as 07.

How many split parts?

Enough distinct insertion gaps must exist in the seed.

Prime run

After the prime run, show the first composite term as a product when factorization is found.

Output and search size

TXT and Excel include all found results, independent of the screen limit.

Digit-split prime patterns

0 patterns tested0 resultsReady
Numbers below 2⁶⁴ receive a deterministic prime check. Larger numbers are labelled probable primes.
Choose a seed range, block length, and split count, then generate.

References

  1. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Lengths 10, 9 and 8, Zenodo, February 8, 2019, pp. 1–175. doi:10.5281/zenodo.2560640 ↗
  2. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 7, Zenodo, February 8, 2019, pp. 1–176. doi:10.5281/zenodo.2560668 ↗
  3. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 6, Zenodo, February 9, 2019, pp. 1–303. doi:10.5281/zenodo.2561096 ↗
  4. Inder J. Taneja, Prime Numbers in Fixed Digits Repetitions Prime Patterns, Zenodo, November 10, 2020, pp. 1–280. doi:10.5281/zenodo.4265818 ↗
  5. Inder J. Taneja, 4-Digits Prime Numbers in Fixed Digits Repetition Prime Patterns, Zenodo, November 29, 2020, pp. 1–1544. doi:10.5281/zenodo.4295652 ↗
  6. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns for 5-Digits Prime Numbers, Zenodo, January 17, 2021, pp. 1–2069. doi:10.5281/zenodo.4445395 ↗

Previous work:

  1. Inder J. Taneja, Patterns in Prime Numbers: Fixed Digits Repetitions, RGMIA Research Report Collection, 20 (2017), Art. 17, pp. 1–75. RGMIA PDF ↗
  2. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – I, RGMIA Research Report Collection, 20 (2017), Art. 73, pp. 1–104. RGMIA PDF ↗
  3. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – II, RGMIA Research Report Collection, 20 (2017), Art. 74, pp. 1–109. RGMIA PDF ↗
  4. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – III, RGMIA Research Report Collection, 20 (2017), Art. 93, pp. 1–113. RGMIA PDF ↗
  5. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – IV, RGMIA Research Report Collection, 20 (2017), Art. 94, pp. 1–150. RGMIA PDF ↗
  6. Inder J. Taneja, Patterns in Prime Numbers: Fixed Digits Repetitions, February 23, 2017. WordPress article ↗