Block #482,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 4:10:50 PM · Difficulty 10.5495 · 6,326,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

407c63b576e577ba903ea1b1301665948589e3148d3c348004b308cc4e48d8d3

View on Chainz ↗

Height

#482,736

Difficulty

10.549451

Transactions

Size

1.43 KB

Version

Bits

0a8ca8d6

Nonce

127,097

Timestamp

4/9/2014, 4:10:50 PM

Confirmations

6,326,738

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a5961c18f3c007e5e5a1bb4a72e76a88aec94eb01ba8d93e877e118e701cc5e0

Transactions (4)

Coinbaseac31ab7161dfef…2fe400550a813b

1 in → 1 out9.0000 XPM110 B

AeKNrjNj…1NEq95Ta

892b56ed70a860…7795b301a49f44

4 in → 10 out36.2200 XPM804 B

ANYbEks7…Feh7syW3 AeKNrjNj…1NEq95Ta ALxaSzoH…c8tfqwKi AcEfJLzo…Ly8aDU8m AMLz4Dj6…KFvw5cVk

f15cca5f7fc4ee…9bf65ff4145668

1 in → 2 out3.4216 XPM226 B

ATQYZ7jv…XC8j6o9k AdtTmX83…PQzgMQS8

dcaa58e6bfc1a7…cb1c49fddfc4c7

1 in → 2 out1.8608 XPM227 B

AcMNnCDo…btimwL4a AeAPnm1g…ZxKdKR61

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.

2.638 × 10¹⁰¹(102-digit number)

26388276503537238878…47256278618344433079

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

2.638 × 10¹⁰¹(102-digit number)

26388276503537238878…47256278618344433079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.638 × 10¹⁰¹(102-digit number)

26388276503537238878…47256278618344433081

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

5.277 × 10¹⁰¹(102-digit number)

52776553007074477757…94512557236688866159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.277 × 10¹⁰¹(102-digit number)

52776553007074477757…94512557236688866161

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

1.055 × 10¹⁰²(103-digit number)

10555310601414895551…89025114473377732319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.055 × 10¹⁰²(103-digit number)

10555310601414895551…89025114473377732321

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

2.111 × 10¹⁰²(103-digit number)

21110621202829791102…78050228946755464639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.111 × 10¹⁰²(103-digit number)

21110621202829791102…78050228946755464641

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

4.222 × 10¹⁰²(103-digit number)

42221242405659582205…56100457893510929279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.222 × 10¹⁰²(103-digit number)

42221242405659582205…56100457893510929281

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 #482,736

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