Block #426,204

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 11:11:04 AM · Difficulty 10.3593 · 6,391,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a8097bc9d88f316bb445d836d1a34b0f78d42bef0b15bafac19ea5262170775

View on Chainz ↗

Height

#426,204

Difficulty

10.359315

Transactions

Size

435 B

Version

Bits

0a5bfc13

Nonce

49,006,045

Timestamp

3/2/2014, 11:11:04 AM

Confirmations

6,391,606

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ff5b1d9c67ce28423fbaf0fde9be75732761ba4f0bd979966d646137e2ff6a68

Transactions (2)

Coinbase19a81c242e13f8…1d04ad25de5c49

1 in → 1 out9.3100 XPM116 B

AbwWkWZt…kawDhufa

2f3d68c93b876e…86c3902b6a774a

1 in → 2 out2.9929 XPM227 B

AR5u1RQQ…6rmieceq AFzWrwda…QXQaTzwX

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.

1.551 × 10¹⁰⁰(101-digit number)

15514256489585440637…55026207660227174399

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

1.551 × 10¹⁰⁰(101-digit number)

15514256489585440637…55026207660227174399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.551 × 10¹⁰⁰(101-digit number)

15514256489585440637…55026207660227174401

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

3.102 × 10¹⁰⁰(101-digit number)

31028512979170881274…10052415320454348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.102 × 10¹⁰⁰(101-digit number)

31028512979170881274…10052415320454348801

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

6.205 × 10¹⁰⁰(101-digit number)

62057025958341762548…20104830640908697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.205 × 10¹⁰⁰(101-digit number)

62057025958341762548…20104830640908697601

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

1.241 × 10¹⁰¹(102-digit number)

12411405191668352509…40209661281817395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.241 × 10¹⁰¹(102-digit number)

12411405191668352509…40209661281817395201

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

2.482 × 10¹⁰¹(102-digit number)

24822810383336705019…80419322563634790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.482 × 10¹⁰¹(102-digit number)

24822810383336705019…80419322563634790401

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 #426,204

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