Problems & Puzzles: Puzzles

Puzzle 1143 Palindromic Prime Pyramid step 3 On set 13, 2023, G.L. Honaker, Jr. sent the following nice puzzle: Palindromic Prime Pyramid 2 3002003 3303002003033 9303303002003033039 7609303303002003033039067 3007609303303002003033039067003 9003007609303303002003033039067003009 3819003007609303303002003033039067003009183 7113819003007609303303002003033039067003009183117 7407113819003007609303303002003033039067003009183117047 1207407113819003007609303303002003033039067003009183117047021 9701207407113819003007609303303002003033039067003009183117047021079 7019701207407113819003007609303303002003033039067003009183117047021079107 … Above are the first 13 rows of a palindromic prime prime pyramid (step size 3) that can eventually end with a 559-digit prime and a total of 94 rows. Calculation shows that the maximum height (number of rows) of such type of pyramid is around 193. See the 94th row here: https://www.utm.edu/staff/caldwell/supplements/ In the same reference we may read this "Starting with 2, there should be one of height around 193 (ending with a 1153 digit prime)". See https://www.utm.edu/staff/caldwell/preprints/JRM_prime_pyramids.pdf   Q. Find a palindromic prime pyramid of step size 3 with a height (number of rows) greater than 94.

---

During the week from 16-23 Set 2023, contributions came from Michael Branicky, J-M Rebert, Giorgos Kalogeropoulos, Oscar Volpatti, Gennady Gusev, Alessandro Casini, Simon Cavegn.

***

Here is a table with the results received. D=6*H-5. Remodeled by CR on March 25, 2026.

Contributor	File	Center digit	Total Digits (D)	Height or rows (H)
Michael	here	2	715	120
Rebert	here	2	625	105
Giorgos	here	2	661	111
Oscar	here	2	691	116
Gennady	here	2	649	109
Alessandro	here	2	691	116
Simon	here	5	739	124