Block #468,707

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 4:42:48 PM · Difficulty 10.4329 · 6,348,040 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed363a4f0cb827f927514a8914a15a4bd4549040b1e0209569e67968baf517d9

View on Chainz ↗

Height

#468,707

Difficulty

10.432881

Transactions

Size

394 B

Version

Bits

0a6ed142

Nonce

27,372

Timestamp

3/31/2014, 4:42:48 PM

Confirmations

6,348,040

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

56cd5fe6a732c2830c2a46b33f3ccc6b7a2548ae5caffc3fea57fd62d10e9e2a

Transactions (2)

Coinbasef9b2cef7d77ada…f9b27a65a7f1f3

1 in → 1 out9.1800 XPM110 B

AeKNrjNj…1NEq95Ta

1154525c57e4b9…bbd05fe85079ba

1 in → 1 out1.0532 XPM192 B

Abs8Q1W2…HYqvgWbJ

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.

8.535 × 10⁹⁸(99-digit number)

85356409553377001226…65551910375591314399

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

8.535 × 10⁹⁸(99-digit number)

85356409553377001226…65551910375591314399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.535 × 10⁹⁸(99-digit number)

85356409553377001226…65551910375591314401

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

1.707 × 10⁹⁹(100-digit number)

17071281910675400245…31103820751182628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.707 × 10⁹⁹(100-digit number)

17071281910675400245…31103820751182628801

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

3.414 × 10⁹⁹(100-digit number)

34142563821350800490…62207641502365257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.414 × 10⁹⁹(100-digit number)

34142563821350800490…62207641502365257601

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

6.828 × 10⁹⁹(100-digit number)

68285127642701600981…24415283004730515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.828 × 10⁹⁹(100-digit number)

68285127642701600981…24415283004730515201

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

1.365 × 10¹⁰⁰(101-digit number)

13657025528540320196…48830566009461030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.365 × 10¹⁰⁰(101-digit number)

13657025528540320196…48830566009461030401

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 #468,707

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