Block #308,706

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 5:51:41 AM · Difficulty 9.9946 · 6,485,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8dbb143837e40f134cab41ef66c48c7481749c204d4b90cd675ba9ac5eff78c3

View on Chainz ↗

Height

#308,706

Difficulty

9.994595

Transactions

Size

1.18 KB

Version

Bits

09fe9dc3

Nonce

103,371

Timestamp

12/13/2013, 5:51:41 AM

Confirmations

6,485,807

Mined by

⛏️ aRQAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9b9dd3dba0e0ba222d3e5b988a6120033965343c5ac556f65802749d02379fb3

Transactions (1)

Coinbase9b9dd3dba0e0ba…02749d02379fb3

1 in → 31 out9.9800 XPM1.09 KB

Aac9Hjdg…P4ktypc3 Aez256Un…NhdMBMc4 AG5YAjec…VhA4Aeh1 AbDHrhkn…fbZN1SRr AZawDE8P…2UydkPDF

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.

6.230 × 10⁹⁴(95-digit number)

62308312162508364565…72174955138202986039

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

6.230 × 10⁹⁴(95-digit number)

62308312162508364565…72174955138202986039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.230 × 10⁹⁴(95-digit number)

62308312162508364565…72174955138202986041

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

1.246 × 10⁹⁵(96-digit number)

12461662432501672913…44349910276405972079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.246 × 10⁹⁵(96-digit number)

12461662432501672913…44349910276405972081

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

2.492 × 10⁹⁵(96-digit number)

24923324865003345826…88699820552811944159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.492 × 10⁹⁵(96-digit number)

24923324865003345826…88699820552811944161

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

4.984 × 10⁹⁵(96-digit number)

49846649730006691652…77399641105623888319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.984 × 10⁹⁵(96-digit number)

49846649730006691652…77399641105623888321

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

9.969 × 10⁹⁵(96-digit number)

99693299460013383304…54799282211247776639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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