Block #306,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 4:29:42 AM · Difficulty 9.9940 · 6,518,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e7aa3671500e63af0496229e2b8cd987895a54c850ad04881a48bf5b94d80f8

View on Chainz ↗

Height

#306,674

Difficulty

9.993950

Transactions

Size

1.11 KB

Version

Bits

09fe7388

Nonce

47,617

Timestamp

12/12/2013, 4:29:42 AM

Confirmations

6,518,884

Mined by

⛏️ aR;ZASWX42VMMDPu9AeW1CGnoamzT3XypQABkY

Merkle Root

3fdc72c7bec4212959d840be57fc7e6d1874e0db9aa5d2243802dd19970263c9

Transactions (1)

Coinbase3fdc72c7bec421…02dd19970263c9

1 in → 29 out9.9800 XPM1.02 KB

ASWX42VM…XypQABkY Ad9pSzHt…cpJ3y2zz AcL1Gy8V…TTnPNdAs AU3a838C…R83Vuk6M AcC2zSod…rtWatH79

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.

4.416 × 10⁹³(94-digit number)

44167577839710817309…00809835744583449599

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

4.416 × 10⁹³(94-digit number)

44167577839710817309…00809835744583449599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.416 × 10⁹³(94-digit number)

44167577839710817309…00809835744583449601

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

8.833 × 10⁹³(94-digit number)

88335155679421634618…01619671489166899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.833 × 10⁹³(94-digit number)

88335155679421634618…01619671489166899201

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

1.766 × 10⁹⁴(95-digit number)

17667031135884326923…03239342978333798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.766 × 10⁹⁴(95-digit number)

17667031135884326923…03239342978333798401

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

3.533 × 10⁹⁴(95-digit number)

35334062271768653847…06478685956667596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.533 × 10⁹⁴(95-digit number)

35334062271768653847…06478685956667596801

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

7.066 × 10⁹⁴(95-digit number)

70668124543537307695…12957371913335193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.066 × 10⁹⁴(95-digit number)

70668124543537307695…12957371913335193601

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 #306,674

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