132 Decimal Digits

Parse 24146959931746498315183988117419243749994763...

24146959931746498315183988117419243749994763...

29922333926938469128211229748433576833895712...

41919171898783211437338163728611572291973121

Parse 132 decimal digits here.

Prime numbers are greater than 1 with only two factors, 1 their respective selves.

You are given a 132-place row of decimal digits formed by concatenating some 24-36 prime numbers each ranging in magnitude from 101 to 999983.

You are asked is to separate the given into its consecutive 3-place, 4-place, 5-place, or 6-place, prime-number components leaving no non-prime numbers in between.

Here is an example:

21152259574687254899263358157527959348745751...

68292812439916827174191259592139276796134847...

51497352457363329377818952125499377274315521

Its twenty-eight consecutive prime-number components are:

211

52259

574687

254899

263

358157

5279

593

487457

516829

281243

991

6827

17419

1259

592139

2767

9613

484751

4973

52457

363329

37781

89521

254993

7727

431

5521

Here is a hint.

Prune the ends in turn until there are none of the original decimal digits remaining.

With respect to the row shown above, 211 is definitely the first component to lop off.

The three alternatives on the left are not prime numbers: 2115, 21152, and 211522.

That was easy.

Okay, so far.

Here is an example of the intrinsic rub.

On the opposite end of the row, 521, 5521, and 315521 are viable candidates inasmuch as all three qualify as prime numbers.

But not 15521, which is profusely factorable: 11, 17, 83, 187, 913, and 1411.

The challenge is to repeatedly work your way out of such predicaments.