Block #305,530

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 1:32:18 PM · Difficulty 9.9936 · 6,505,397 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a51009c48b059aac9c210eb87a8ffde31b2ed451d55629910ecddc01427a6df9

View on Chainz ↗

Height

#305,530

Difficulty

9.993603

Transactions

Size

1.51 KB

Version

Bits

09fe5cc8

Nonce

30,022

Timestamp

12/11/2013, 1:32:18 PM

Confirmations

6,505,397

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

dc3eea3b9ea81f2bee942b6d9405f927b9fcae4b64b469dc5173a1d7f2093045

Transactions (5)

Coinbase7400cd2cb3c571…bd931a2c59cd6c

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

43ace6e9ce8e91…8820965c159741

3 in → 2 out10.2008 XPM520 B

AUvFDX1j…PgjQN5u7 AMR3Ty2B…FEJC8DUt

7f74b588398b9b…f199730eca5db6

1 in → 2 out4.8457 XPM226 B

AdPxK7Xb…oRhhbocC AanspCyf…cGBV86zu

c8accfd11f071e…bef95791e3d18c

1 in → 2 out1.8303 XPM225 B

AQtfdk1i…ZcpYzmGg AUZ2tw2m…3MDXhqbV

14552d633685e8…19d017884ad9ff

2 in → 2 out2.0518 XPM373 B

AQLgQ1R4…YyexwkDf AQnUr4Hn…tmKt2HQL

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.

3.102 × 10⁹⁵(96-digit number)

31028963705638227867…14562383691171391999

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

3.102 × 10⁹⁵(96-digit number)

31028963705638227867…14562383691171391999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.102 × 10⁹⁵(96-digit number)

31028963705638227867…14562383691171392001

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

6.205 × 10⁹⁵(96-digit number)

62057927411276455734…29124767382342783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.205 × 10⁹⁵(96-digit number)

62057927411276455734…29124767382342784001

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

1.241 × 10⁹⁶(97-digit number)

12411585482255291146…58249534764685567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.241 × 10⁹⁶(97-digit number)

12411585482255291146…58249534764685568001

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

2.482 × 10⁹⁶(97-digit number)

24823170964510582293…16499069529371135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.482 × 10⁹⁶(97-digit number)

24823170964510582293…16499069529371136001

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

4.964 × 10⁹⁶(97-digit number)

49646341929021164587…32998139058742271999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.964 × 10⁹⁶(97-digit number)

49646341929021164587…32998139058742272001

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 #305,530

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