Block #464,961

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 3:33:33 AM · Difficulty 10.4229 · 6,336,840 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

edbc1cf657ba5b52e5ffc7591fc6a48d6ec0095e80dd1cefbc3f139eee70f265

View on Chainz ↗

Height

#464,961

Difficulty

10.422948

Transactions

Size

726 B

Version

Bits

0a6c4655

Nonce

205,144

Timestamp

3/29/2014, 3:33:33 AM

Confirmations

6,336,840

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

22184bc7345e7bb9671b9adf9ace876b9d73b7ae48a665e28caf44963c40e5c5

Transactions (2)

Coinbase3a421372825a9b…3c1e0f93c96fe1

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

b568f6e7dc316e…781af950e2cf2c

3 in → 2 out1205.6000 XPM522 B

ASQvCg4A…hQn3kS8p ATMdQaqJ…V1pGVNKf

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.

1.568 × 10¹⁰⁴(105-digit number)

15686951758343941817…44890381106651699199

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

1.568 × 10¹⁰⁴(105-digit number)

15686951758343941817…44890381106651699199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.568 × 10¹⁰⁴(105-digit number)

15686951758343941817…44890381106651699201

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

3.137 × 10¹⁰⁴(105-digit number)

31373903516687883635…89780762213303398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.137 × 10¹⁰⁴(105-digit number)

31373903516687883635…89780762213303398401

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

6.274 × 10¹⁰⁴(105-digit number)

62747807033375767271…79561524426606796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.274 × 10¹⁰⁴(105-digit number)

62747807033375767271…79561524426606796801

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

1.254 × 10¹⁰⁵(106-digit number)

12549561406675153454…59123048853213593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.254 × 10¹⁰⁵(106-digit number)

12549561406675153454…59123048853213593601

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

2.509 × 10¹⁰⁵(106-digit number)

25099122813350306908…18246097706427187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.509 × 10¹⁰⁵(106-digit number)

25099122813350306908…18246097706427187201

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