Block #374,538

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 2:41:23 AM · Difficulty 10.4215 · 6,433,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e20c652497ea74731abcd34fc358bb78e52c329fd6f6e60df5b9fe0d49434f1

View on Chainz ↗

Height

#374,538

Difficulty

10.421489

Transactions

Size

1.08 KB

Version

Bits

0a6be6b3

Nonce

56,345

Timestamp

1/25/2014, 2:41:23 AM

Confirmations

6,433,916

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1579f784a6189c6adf9c82d9e32058ca88e74c2db0b9c8a5fecedc20d9840b27

Transactions (5)

Coinbase48ac372a89ebc0…30337fa17974d9

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

fe70a824ba1d24…7055db21709d25

1 in → 2 out4.0967 XPM226 B

AVARj4Kc…2AeNp5Gi AWmXJys9…mUqbyCVk

1e6e1992bbf237…df368a46ae09ed

1 in → 2 out1.0746 XPM226 B

AYVyegUo…88drMYWV AdcvgzfG…ErN9aPBM

d14650c246ac49…a041ad7d6ffe46

1 in → 2 out2.1089 XPM227 B

AcTfgs3n…wEgwN1w8 AVbydi7Y…5pWtdGgJ

d6ee7e2b216e03…0cf52f1444b5d3

1 in → 2 out1.9061 XPM227 B

AQ3Ukc2C…WWEuH8x3 AaEcoCKy…7ij9ba5e

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.

1.291 × 10⁹⁹(100-digit number)

12914324803336635310…97567487291334590399

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

1.291 × 10⁹⁹(100-digit number)

12914324803336635310…97567487291334590399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.291 × 10⁹⁹(100-digit number)

12914324803336635310…97567487291334590401

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

2.582 × 10⁹⁹(100-digit number)

25828649606673270620…95134974582669180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.582 × 10⁹⁹(100-digit number)

25828649606673270620…95134974582669180801

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

5.165 × 10⁹⁹(100-digit number)

51657299213346541241…90269949165338361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.165 × 10⁹⁹(100-digit number)

51657299213346541241…90269949165338361601

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

1.033 × 10¹⁰⁰(101-digit number)

10331459842669308248…80539898330676723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.033 × 10¹⁰⁰(101-digit number)

10331459842669308248…80539898330676723201

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

2.066 × 10¹⁰⁰(101-digit number)

20662919685338616496…61079796661353446399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.066 × 10¹⁰⁰(101-digit number)

20662919685338616496…61079796661353446401

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 #374,538

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