Block #156,327

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 9:12:22 PM · Difficulty 9.8685 · 6,636,317 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12fefa2a786ddfb7c991c6884c838105620134a425d1e83b5942efe321f08f31

View on Chainz ↗

Height

#156,327

Difficulty

9.868481

Transactions

Size

197 B

Version

Bits

09de54be

Nonce

75,231

Timestamp

9/8/2013, 9:12:22 PM

Confirmations

6,636,317

Merkle Root

c1d89b49a8bd85de763f9308e713b04c83fe03e1cd44e0cb90805b19899c8b1b

Transactions (1)

Coinbasec1d89b49a8bd85…805b19899c8b1b

1 in → 1 out10.2500 XPM109 B

AJn9y9Wv…G4raUX4o

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.

1.566 × 10⁹⁰(91-digit number)

15661433969218195068…06877090791083689519

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

1.566 × 10⁹⁰(91-digit number)

15661433969218195068…06877090791083689519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.566 × 10⁹⁰(91-digit number)

15661433969218195068…06877090791083689521

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

3.132 × 10⁹⁰(91-digit number)

31322867938436390137…13754181582167379039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.132 × 10⁹⁰(91-digit number)

31322867938436390137…13754181582167379041

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

6.264 × 10⁹⁰(91-digit number)

62645735876872780275…27508363164334758079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.264 × 10⁹⁰(91-digit number)

62645735876872780275…27508363164334758081

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

1.252 × 10⁹¹(92-digit number)

12529147175374556055…55016726328669516159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10⁹¹(92-digit number)

12529147175374556055…55016726328669516161

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

2.505 × 10⁹¹(92-digit number)

25058294350749112110…10033452657339032319

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