Block #345,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/6/2014, 12:27:56 AM · Difficulty 10.2110 · 6,470,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d4830a0f7280d5a3c49323fea210527be639157b5c2e9ba00e219bd70b8e772

View on Chainz ↗

Height

#345,557

Difficulty

10.210982

Transactions

Size

1.01 KB

Version

Bits

0a3602e7

Nonce

72,353

Timestamp

1/6/2014, 12:27:56 AM

Confirmations

6,470,857

Mined by

⛏️ EaRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

11001e71de5fd604d6354f8804443f182f46ef0c8823b26232eb05999be0b289

Transactions (1)

Coinbase11001e71de5fd6…eb05999be0b289

1 in → 26 out9.5705 XPM947 B

AQwRN8bE…V8PsTcY9 AGZ2JBW7…PB8PfHtw AbFpBLvY…B3viNUcX AYtDvcGs…VuAcA7m7 AKFkBomb…mNFp4GuE

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.

4.792 × 10⁹⁹(100-digit number)

47923071190126461423…92929712178144383879

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

4.792 × 10⁹⁹(100-digit number)

47923071190126461423…92929712178144383879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.792 × 10⁹⁹(100-digit number)

47923071190126461423…92929712178144383881

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

9.584 × 10⁹⁹(100-digit number)

95846142380252922846…85859424356288767759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.584 × 10⁹⁹(100-digit number)

95846142380252922846…85859424356288767761

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

1.916 × 10¹⁰⁰(101-digit number)

19169228476050584569…71718848712577535519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.916 × 10¹⁰⁰(101-digit number)

19169228476050584569…71718848712577535521

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

3.833 × 10¹⁰⁰(101-digit number)

38338456952101169138…43437697425155071039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.833 × 10¹⁰⁰(101-digit number)

38338456952101169138…43437697425155071041

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

7.667 × 10¹⁰⁰(101-digit number)

76676913904202338277…86875394850310142079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.667 × 10¹⁰⁰(101-digit number)

76676913904202338277…86875394850310142081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.533 × 10¹⁰¹(102-digit number)

15335382780840467655…73750789700620284159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #345,557

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