Block #482,234

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 9:22:24 AM · Difficulty 10.5413 · 6,313,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96b1cf6391a8fc0bb8c91a9a598f5c0665f5698fb3f3cc5b40601ffe3b032df7

View on Chainz ↗

Height

#482,234

Difficulty

10.541295

Transactions

Size

5.98 KB

Version

Bits

0a8a9248

Nonce

122,362

Timestamp

4/9/2014, 9:22:24 AM

Confirmations

6,313,751

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

631307db5dceaaeb9a69e1bd1e87fd500c10ebf2aadda75d4c0bf43b4831cf41

Transactions (5)

Coinbase1f9121c7e60f35…385ed4e8c99925

1 in → 3 out9.0800 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

d08da97956c862…2d923f2b3d8962

35 in → 1 out35.0575 XPM5.10 KB

Aa5WzsJY…BDkGXVYs

b4eb0d313bee62…4f19a7d6100454

1 in → 1 out3.0748 XPM192 B

AM83jLyW…bPX2KoDr

fb3a297ca9cf51…ed60404f4bd414

1 in → 2 out3.9610 XPM226 B

AJ5V9U1m…oDgoTEq9 APpTpGhZ…fLioJSac

128d09f41a0827…561f99437e7367

1 in → 2 out1.8938 XPM226 B

AQXHTLWN…SGHsgNvK AYC5FTEV…8Hi4WYtv

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.

1.289 × 10⁹⁵(96-digit number)

12894877183481098683…22865456445674776599

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

1.289 × 10⁹⁵(96-digit number)

12894877183481098683…22865456445674776599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.289 × 10⁹⁵(96-digit number)

12894877183481098683…22865456445674776601

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

2.578 × 10⁹⁵(96-digit number)

25789754366962197366…45730912891349553199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.578 × 10⁹⁵(96-digit number)

25789754366962197366…45730912891349553201

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

5.157 × 10⁹⁵(96-digit number)

51579508733924394732…91461825782699106399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.157 × 10⁹⁵(96-digit number)

51579508733924394732…91461825782699106401

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

1.031 × 10⁹⁶(97-digit number)

10315901746784878946…82923651565398212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.031 × 10⁹⁶(97-digit number)

10315901746784878946…82923651565398212801

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

2.063 × 10⁹⁶(97-digit number)

20631803493569757893…65847303130796425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.063 × 10⁹⁶(97-digit number)

20631803493569757893…65847303130796425601

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