Block #261,944

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/16/2013, 8:22:24 AM · Difficulty 9.9701 · 6,541,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

425c17773babc69d8c3f15658448f7b0bee77e6f071dd3d5d317b099b6ffa5e2

View on Chainz ↗

Height

#261,944

Difficulty

9.970124

Transactions

Size

2.01 KB

Version

Bits

09f85a13

Nonce

289,597

Timestamp

11/16/2013, 8:22:24 AM

Confirmations

6,541,832

Mined by

⛏️ 8aR*ARXSrG7zDJaFCruTxsaP6YvsvPCRW69WR4

Merkle Root

8b48bb9ec2ee6c08ba89d0aaeb36f1b8ec10b823663b13e5afcddb644f2f420d

Transactions (1)

Coinbase8b48bb9ec2ee6c…cddb644f2f420d

1 in → 56 out10.0200 XPM1.92 KB

ARXSrG7z…CRW69WR4 AFqKfjez…qX9Ace3g APH8rV6F…heb1HF2Z AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC

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.

7.016 × 10⁹⁰(91-digit number)

70165084057610345942…47209692607270462639

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

7.016 × 10⁹⁰(91-digit number)

70165084057610345942…47209692607270462639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.016 × 10⁹⁰(91-digit number)

70165084057610345942…47209692607270462641

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

1.403 × 10⁹¹(92-digit number)

14033016811522069188…94419385214540925279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.403 × 10⁹¹(92-digit number)

14033016811522069188…94419385214540925281

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

2.806 × 10⁹¹(92-digit number)

28066033623044138376…88838770429081850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.806 × 10⁹¹(92-digit number)

28066033623044138376…88838770429081850561

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

5.613 × 10⁹¹(92-digit number)

56132067246088276753…77677540858163701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.613 × 10⁹¹(92-digit number)

56132067246088276753…77677540858163701121

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

1.122 × 10⁹²(93-digit number)

11226413449217655350…55355081716327402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.122 × 10⁹²(93-digit number)

11226413449217655350…55355081716327402241

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