Block #323,096

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 10:25:45 AM · Difficulty 10.2012 · 6,491,204 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76697609b1dff8502732304dde8e185120dbbf9aa9c67e10d047d50d195eaaed

View on Chainz ↗

Height

#323,096

Difficulty

10.201151

Transactions

Size

1003 B

Version

Bits

0a337e9f

Nonce

13,617

Timestamp

12/21/2013, 10:25:45 AM

Confirmations

6,491,204

Mined by

⛏️ aRm6AQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

2b43b575d861d27cf44dd18cad4c6ca6c3f08b627c47858d0340dc35e99d533e

Transactions (1)

Coinbase2b43b575d861d2…40dc35e99d533e

1 in → 25 out9.5900 XPM913 B

AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 ASWX42VM…XypQABkY Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz

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.

1.694 × 10⁹⁴(95-digit number)

16942103736363737031…73711503541651740399

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

1.694 × 10⁹⁴(95-digit number)

16942103736363737031…73711503541651740399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.694 × 10⁹⁴(95-digit number)

16942103736363737031…73711503541651740401

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

3.388 × 10⁹⁴(95-digit number)

33884207472727474063…47423007083303480799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.388 × 10⁹⁴(95-digit number)

33884207472727474063…47423007083303480801

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

6.776 × 10⁹⁴(95-digit number)

67768414945454948127…94846014166606961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.776 × 10⁹⁴(95-digit number)

67768414945454948127…94846014166606961601

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

1.355 × 10⁹⁵(96-digit number)

13553682989090989625…89692028333213923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.355 × 10⁹⁵(96-digit number)

13553682989090989625…89692028333213923201

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

2.710 × 10⁹⁵(96-digit number)

27107365978181979250…79384056666427846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.710 × 10⁹⁵(96-digit number)

27107365978181979250…79384056666427846401

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 #323,096

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