Block #171,422

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/19/2013, 11:55:28 AM · Difficulty 9.8642 · 6,640,892 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

3413d3541e1f089a311afc8cd731a8fa2b54ad62c8cbb5922c6ec234763b1649

View on Chainz ↗

Height

#171,422

Difficulty

9.864238

Transactions

Size

587 B

Version

Bits

09dd3eae

Nonce

168,179

Timestamp

9/19/2013, 11:55:28 AM

Confirmations

6,640,892

Mined by

⛏️ P2SHAM9T3kkVfNGKZTaEoAaDSM5fqWm9jwFuUw

Merkle Root

c37094ca1415494e942acad5331b08216721168fa0bb1c28cfe104e496debeb4

Transactions (2)

Coinbasec7afd51cab69bf…e5348e14514e71

1 in → 1 out10.2700 XPM109 B

AM9T3kkV…m9jwFuUw

fc4e0aa269822a…36f8142cc5fb79

3 in → 1 out30.8300 XPM386 B

AMfUufeM…gqTpCamv

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.658 × 10⁹⁸(99-digit number)

26580184668082847014…83911927852939042319

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.658 × 10⁹⁸(99-digit number)

26580184668082847014…83911927852939042319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.658 × 10⁹⁸(99-digit number)

26580184668082847014…83911927852939042321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.316 × 10⁹⁸(99-digit number)

53160369336165694029…67823855705878084639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.316 × 10⁹⁸(99-digit number)

53160369336165694029…67823855705878084641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.063 × 10⁹⁹(100-digit number)

10632073867233138805…35647711411756169279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.063 × 10⁹⁹(100-digit number)

10632073867233138805…35647711411756169281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.126 × 10⁹⁹(100-digit number)

21264147734466277611…71295422823512338559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.126 × 10⁹⁹(100-digit number)

21264147734466277611…71295422823512338561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.252 × 10⁹⁹(100-digit number)

42528295468932555223…42590845647024677119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #171,422

Cookie Preferences