Block #462,889

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 5:48:47 PM · Difficulty 10.4164 · 6,345,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

003e583f9e226ca25885722711596f6870be1c54a1bce357bfb97ea7c478b789

View on Chainz ↗

Height

#462,889

Difficulty

10.416442

Transactions

Size

858 B

Version

Bits

0a6a9bf0

Nonce

290,412

Timestamp

3/27/2014, 5:48:47 PM

Confirmations

6,345,331

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

63fa24a567d1d5a7af2e18e0e2aadbf7ab4f3640a1e97484099c6dcfe665dbbc

Transactions (2)

Coinbase495e15360733a1…f103b8f53f32d7

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

7a0b6af8554542…435ae0f63a9c7b

3 in → 9 out27.6200 XPM658 B

AbSLdNfP…EdKJ1eS4 AZSVhd9Y…rYTSwNV1 AQdWTjRq…j7iXMVXt AUyZ4pNB…FBGJSpD9 AeKNrjNj…1NEq95Ta

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.

1.307 × 10⁹⁵(96-digit number)

13079468755721303207…86736789749495398399

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

1.307 × 10⁹⁵(96-digit number)

13079468755721303207…86736789749495398399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.307 × 10⁹⁵(96-digit number)

13079468755721303207…86736789749495398401

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

2.615 × 10⁹⁵(96-digit number)

26158937511442606415…73473579498990796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.615 × 10⁹⁵(96-digit number)

26158937511442606415…73473579498990796801

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

5.231 × 10⁹⁵(96-digit number)

52317875022885212831…46947158997981593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.231 × 10⁹⁵(96-digit number)

52317875022885212831…46947158997981593601

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

1.046 × 10⁹⁶(97-digit number)

10463575004577042566…93894317995963187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.046 × 10⁹⁶(97-digit number)

10463575004577042566…93894317995963187201

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

2.092 × 10⁹⁶(97-digit number)

20927150009154085132…87788635991926374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.092 × 10⁹⁶(97-digit number)

20927150009154085132…87788635991926374401

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 #462,889

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