Block #483,316

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 11:47:09 PM · Difficulty 10.5611 · 6,313,495 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93c29388c8c7b4b746b29e1bf708b1bfc883a320af74fd037b0eec82cae6163d

View on Chainz ↗

Height

#483,316

Difficulty

10.561068

Transactions

Size

1.71 KB

Version

Bits

0a8fa225

Nonce

5,547

Timestamp

4/9/2014, 11:47:09 PM

Confirmations

6,313,495

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d3eaae9f04f1a029fb185a7cea82d7981a7fb3cf636523900321142775f6b234

Transactions (3)

Coinbaseb08e8e7df0fbc2…90b026fb59e59f

1 in → 1 out8.9800 XPM110 B

AeKNrjNj…1NEq95Ta

683ca44718c790…a86abd73f34eac

6 in → 14 out48.3657 XPM1.18 KB

Af2gGhPs…PKt5R2Nm AZwYHhVa…1Z4DC5JF AXmcBRtB…f1EMXBhR AQtisFei…VwsPGKH9 AHWcE641…mx64JLTa

968f8289c5f033…6ec417897dad06

2 in → 1 out0.9965 XPM339 B

AG88DweJ…QeQTqESq

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.

1.481 × 10¹⁰⁰(101-digit number)

14814301182117616649…25932256285175684399

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

1.481 × 10¹⁰⁰(101-digit number)

14814301182117616649…25932256285175684399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.481 × 10¹⁰⁰(101-digit number)

14814301182117616649…25932256285175684401

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

2.962 × 10¹⁰⁰(101-digit number)

29628602364235233299…51864512570351368799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.962 × 10¹⁰⁰(101-digit number)

29628602364235233299…51864512570351368801

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

5.925 × 10¹⁰⁰(101-digit number)

59257204728470466599…03729025140702737599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.925 × 10¹⁰⁰(101-digit number)

59257204728470466599…03729025140702737601

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

1.185 × 10¹⁰¹(102-digit number)

11851440945694093319…07458050281405475199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.185 × 10¹⁰¹(102-digit number)

11851440945694093319…07458050281405475201

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

2.370 × 10¹⁰¹(102-digit number)

23702881891388186639…14916100562810950399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.370 × 10¹⁰¹(102-digit number)

23702881891388186639…14916100562810950401

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