Puzzle 1262 Pilish primes

Puzzle 1262 Pilish primes

Today is another pi-day, March 14, (3.14), 2026.

Photo provided by my friend G. L. Honaker Jr. Original by Holly Rolen, of "Just Pie"

Carlos Rivera has constructed this puzzle, celebrating this popular day...

Introduction.

Have you heard about the Pilish languaje?

In the 7th paragraph of this page you may read a short introduction to Pilish:

"... In “Pi-lish” the number of letters in each word match the corresponding digit of pi. This first word has three letters, the second has one letter, the third has four letters, and so on. This language is more popular than you might think. Software engineer Michael Keith wrote an entire book, called Not a Wake in this language."

Just in case you need another explanation see this other page from the BBC "How the number pi inspired a writing style".

***

Our puzzle.

Regarding that pi = 3.14159265358979323846264338327950...

In this puzzle we will change the words composed by k letters, by primes composed by k digits, where k₁=3 digits, k₂=1 digits, k₃=4 digits, ... Moreover, we will ask to form primes linking n prime-words, in such a way that every new linkage forms a new prime. This is what I will call from now on, "Pilish primes"

The 1st valid prime-word has k₁=3 digits, or any of the following 143 primes {101, 103, 107, 109, ... 991, 997]
The 2nd valid prime-word has k₂=1 digits, or any of the following 2 primes {3, 7}
The 3rd valid prime word has k₃=4 digits, or any of the following 1061 primes {1009, 1013, 1019, ..., 9967, 9973}
...
The 32nd valid prime word has k₃₂=5 digits, or any of the following 8363 primes {10007, 10009. ..., 99989, 99991 }

But there is no 33nd valid prime word because in the position 33rd emerges a "zero" in pi.

According with this, here is an example of a phrase of three words:
101 is a valid one word prime
101.3 is a valid two linked prime-words because 101 & 3 and 1013 are three primes
101.3.1019 is a valid phrase composed by three linked prime-words because 101, 3, 1019, 1013 and 10131019 are five primes, and a total of 8 digits in the phrase 101.3.1019.

...

In short for n primes linked you produce a total of 2*n-1 primes.

Now, because the digit "0" is located in the 33rd position (counting the initial digit "3" of pi) the largest prime we may form is composed by 32 linked distinct prime-words composed by 3, 1, 4, ...9, 5 digits, then the largest valid linked prime-words you may form after linking these 32 prime-words has 155 digits, which is the sum of all the pi digits before the digit "0".

Moreover, the prime linking 32 distinct prime-words produces in total 2*32-1 = 63 primes.

I do not know for certain if this kind of beatiful prime-monsters exist but I bet that the answer is yes... wHY?... because the digit "1" in pi comes only two times in the first 32 digits, and these two "1" digits are at the beginning of pi (positions 2 & 4), fortunately not together, and I suppose that they produce the less constriction possible in such positions... (I hope, fingers crossed).

Enough?

The questions

Q1. Find the smallest valid phrase linking 32 distinct word primes, composed of 155 digits and producing a total of 63 primes.
Q2. Find the largest valid phrase linking 32 distinct word primes, composed of 155 digits and producing a total of 63 primes.

or, in short:

Q1. Find the smallest Pilish prime of 155 digits (using only distinct primes)
Q2. Find the largest Pilish prime of 155 digits (using only distinct primes)

101.3.1019.7.10391.100000969.41.100207.10973.103.10259.10000687.100002509.1000423.100023221.991.53.229.10003457.1153.109169.43.100517.1453.683.787.10101167.163.23.1012159.100003157.11497. 1000192133.37.10000583.10005379.5147