Block #478,646

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 5:28:24 AM · Difficulty 10.4947 · 6,316,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4bd3fb73b94fdf5c8b0c40e756c31a447f99c31b398d968b5a95a89728ef4d3

View on Chainz ↗

Height

#478,646

Difficulty

10.494727

Transactions

Size

823 B

Version

Bits

0a7ea668

Nonce

161,653

Timestamp

4/7/2014, 5:28:24 AM

Confirmations

6,316,244

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

067c614d15cd4e7adff122bd69da1d47e96b37f4c190be4d536fbd73ea4c7322

Transactions (2)

Coinbase45a85709ffcdea…ba1a34fcb5f375

1 in → 1 out9.0800 XPM110 B

AeKNrjNj…1NEq95Ta

e11f1bb2f076b0…03bcaf52c4838f

3 in → 7 out20.6199 XPM624 B

AeKNrjNj…1NEq95Ta AesAVNRf…eAXARtnF ALVnDkGf…DmNDEGCn AYhUoV9Q…wNVDEKRP AQgZKPra…nwpjY1Ad

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.

1.092 × 10⁹³(94-digit number)

10926350598434485681…57092855822435457749

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

1.092 × 10⁹³(94-digit number)

10926350598434485681…57092855822435457749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.092 × 10⁹³(94-digit number)

10926350598434485681…57092855822435457751

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

2.185 × 10⁹³(94-digit number)

21852701196868971362…14185711644870915499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.185 × 10⁹³(94-digit number)

21852701196868971362…14185711644870915501

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

4.370 × 10⁹³(94-digit number)

43705402393737942725…28371423289741830999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.370 × 10⁹³(94-digit number)

43705402393737942725…28371423289741831001

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

8.741 × 10⁹³(94-digit number)

87410804787475885450…56742846579483661999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.741 × 10⁹³(94-digit number)

87410804787475885450…56742846579483662001

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

1.748 × 10⁹⁴(95-digit number)

17482160957495177090…13485693158967323999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.748 × 10⁹⁴(95-digit number)

17482160957495177090…13485693158967324001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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