Block #215,629

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 5:28:02 AM · Difficulty 9.9255 · 6,595,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a929a60de905a071611770d1420ee9d178afe7950f413a21ed36779780b341f

View on Chainz ↗

Height

#215,629

Difficulty

9.925457

Transactions

Size

5.17 KB

Version

Bits

09eceac6

Nonce

1,164,998,568

Timestamp

10/18/2013, 5:28:02 AM

Confirmations

6,595,491

Mined by

⛏️ MJR`.xAUqensbe6x6mWTjN61oyi6VYvaXkkpa1EE

Merkle Root

8cd81e2c06b1aacbd121ca2bae853dd72fda1e80f7fa8d9efcdc9a13ad1e0bd9

Transactions (1)

Coinbase8cd81e2c06b1aa…dc9a13ad1e0bd9

1 in → 151 out10.0800 XPM5.07 KB

AUqensbe…Xkkpa1EE AK61Jfjk…fenNk1MA Ac2cAFSv…5JnaUMRc Ab8m6NAW…vmj4QCfy AeMCN6pE…zNDvzECH

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.

1.642 × 10¹⁰²(103-digit number)

16421449404270365559…61548178278239057919

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

1.642 × 10¹⁰²(103-digit number)

16421449404270365559…61548178278239057919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.642 × 10¹⁰²(103-digit number)

16421449404270365559…61548178278239057921

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

3.284 × 10¹⁰²(103-digit number)

32842898808540731118…23096356556478115839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.284 × 10¹⁰²(103-digit number)

32842898808540731118…23096356556478115841

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

6.568 × 10¹⁰²(103-digit number)

65685797617081462237…46192713112956231679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.568 × 10¹⁰²(103-digit number)

65685797617081462237…46192713112956231681

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

1.313 × 10¹⁰³(104-digit number)

13137159523416292447…92385426225912463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.313 × 10¹⁰³(104-digit number)

13137159523416292447…92385426225912463361

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

2.627 × 10¹⁰³(104-digit number)

26274319046832584894…84770852451824926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.627 × 10¹⁰³(104-digit number)

26274319046832584894…84770852451824926721

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 #215,629

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