Block #479,247

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 1:55:33 PM · Difficulty 10.5034 · 6,334,901 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

811cc286e168cd60870e5a1d08f5c25325e2a399438c16b932fc8568d65fe5d9

View on Chainz ↗

Height

#479,247

Difficulty

10.503431

Transactions

Size

948 B

Version

Bits

0a80e0e1

Nonce

45,202

Timestamp

4/7/2014, 1:55:33 PM

Confirmations

6,334,901

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1fdc27be065d2c695734dd0d283f19d68efedd048edd5913e4d26bbee6976249

Transactions (3)

Coinbasef1e01cd07d6130…4883bfdb8b7de1

1 in → 1 out9.0700 XPM110 B

AeKNrjNj…1NEq95Ta

8b078d22aed226…303a30aa302456

3 in → 2 out6.1663 XPM521 B

AVrNG5M4…jyNAdVLo ALbqPTBL…RZv6Jjce

c85ebc6c0819e8…b1df34283721b2

1 in → 2 out2.2140 XPM225 B

AcQfxVUD…vQnNph4X AbofBK6y…26BnxJ4w

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.

1.183 × 10⁹⁹(100-digit number)

11836898703033041831…01107310423268590239

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

1.183 × 10⁹⁹(100-digit number)

11836898703033041831…01107310423268590239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.183 × 10⁹⁹(100-digit number)

11836898703033041831…01107310423268590241

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

2.367 × 10⁹⁹(100-digit number)

23673797406066083663…02214620846537180479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.367 × 10⁹⁹(100-digit number)

23673797406066083663…02214620846537180481

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

4.734 × 10⁹⁹(100-digit number)

47347594812132167326…04429241693074360959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.734 × 10⁹⁹(100-digit number)

47347594812132167326…04429241693074360961

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

9.469 × 10⁹⁹(100-digit number)

94695189624264334653…08858483386148721919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.469 × 10⁹⁹(100-digit number)

94695189624264334653…08858483386148721921

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

1.893 × 10¹⁰⁰(101-digit number)

18939037924852866930…17716966772297443839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.893 × 10¹⁰⁰(101-digit number)

18939037924852866930…17716966772297443841

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

Block #479,247

Cookie Preferences