Block #186,128

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 5:41:52 PM · Difficulty 9.8642 · 6,608,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15a63e24f740dc78b0a60cb4fe01ab73a42e3b8ceb9ff9033eaaf4df6b459db8

View on Chainz ↗

Height

#186,128

Difficulty

9.864225

Transactions

Size

1.64 KB

Version

Bits

09dd3dde

Nonce

21,907

Timestamp

9/29/2013, 5:41:52 PM

Confirmations

6,608,012

Merkle Root

ca63a1ce60a023c3494f615edb963e59319d2d5d2a43c74716405af96c3f2104

Transactions (5)

Coinbasee42a71095d5bdf…32f8d399cdaaa0

1 in → 1 out10.3100 XPM109 B

AKyKBBF5…Q9vxBLNg

9ebcc02f7b7adc…66b01c00b56e07

2 in → 7 out20.5400 XPM474 B

ARTJCDz1…oJ6Hi1d9 ALd5yTY2…vgfAFVPZ AHADV2Ly…7mcKNDYV AQAdmZHM…DAr5ycEL AY8aJCxo…ymnUSycu

0a43ab13a3b6d7…f044f4dcf60a9a

2 in → 2 out10.7291 XPM372 B

ALpthvGg…D1g5z4CT Abr41vbA…4CxXA4oT

75bc4f49b52d50…ce879306c016ab

2 in → 4 out12.7658 XPM407 B

ANvtpRa1…QjsraDJz ANAVEjQm…6wqP126u AQXUSoBL…CzbjKp8b AZ4QAejN…gwqGZDtJ

9edb8375c7e40a…8dd06d84d5b1c9

1 in → 2 out5.5646 XPM225 B

AcyPVp7N…dDULWcdA ANvtpRa1…QjsraDJz

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.

6.056 × 10⁹³(94-digit number)

60560406419766945636…18433126503495508679

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

6.056 × 10⁹³(94-digit number)

60560406419766945636…18433126503495508679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.056 × 10⁹³(94-digit number)

60560406419766945636…18433126503495508681

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

1.211 × 10⁹⁴(95-digit number)

12112081283953389127…36866253006991017359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.211 × 10⁹⁴(95-digit number)

12112081283953389127…36866253006991017361

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

2.422 × 10⁹⁴(95-digit number)

24224162567906778254…73732506013982034719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.422 × 10⁹⁴(95-digit number)

24224162567906778254…73732506013982034721

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

4.844 × 10⁹⁴(95-digit number)

48448325135813556509…47465012027964069439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.844 × 10⁹⁴(95-digit number)

48448325135813556509…47465012027964069441

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

9.689 × 10⁹⁴(95-digit number)

96896650271627113018…94930024055928138879

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