Block #425,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 1:49:34 AM · Difficulty 10.3586 · 6,401,013 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a0578a37ceedd30d468382c298f5424965308a9bed60bb8fded6296291bd83e

View on Chainz ↗

Height

#425,636

Difficulty

10.358592

Transactions

Size

1.26 KB

Version

Bits

0a5bccaf

Nonce

629,816

Timestamp

3/2/2014, 1:49:34 AM

Confirmations

6,401,013

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0b5a5d2ad5d77e32785008d1fb5f8d2b1192a91ab7e03e482619907359c97c6a

Transactions (2)

Coinbase05a6c905fcb4c1…95dd69f5303ed5

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

6aaa32b2b24a17…7476c901746a47

5 in → 15 out46.3500 XPM1.06 KB

AW312AG1…u6JA7wrR AGfsMhfv…2d8ABBPD AXj9dTBU…zToBoMyP AaGkJXq9…iVUx3jP9 AMUH1Z1t…Q1XW99zU

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.

1.181 × 10⁹⁴(95-digit number)

11817091524265206165…66421293846960878319

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

1.181 × 10⁹⁴(95-digit number)

11817091524265206165…66421293846960878319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.181 × 10⁹⁴(95-digit number)

11817091524265206165…66421293846960878321

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

2.363 × 10⁹⁴(95-digit number)

23634183048530412330…32842587693921756639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.363 × 10⁹⁴(95-digit number)

23634183048530412330…32842587693921756641

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

4.726 × 10⁹⁴(95-digit number)

47268366097060824661…65685175387843513279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.726 × 10⁹⁴(95-digit number)

47268366097060824661…65685175387843513281

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

9.453 × 10⁹⁴(95-digit number)

94536732194121649322…31370350775687026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.453 × 10⁹⁴(95-digit number)

94536732194121649322…31370350775687026561

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

1.890 × 10⁹⁵(96-digit number)

18907346438824329864…62740701551374053119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.890 × 10⁹⁵(96-digit number)

18907346438824329864…62740701551374053121

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 #425,636

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