Block #262,472

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/16/2013, 9:25:53 PM · Difficulty 9.9686 · 6,545,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1197fe3bdb0f9ec12062623910b53a5954ceee9ce0635f2f7f68261ed4d2d426

View on Chainz ↗

Height

#262,472

Difficulty

9.968586

Transactions

Size

2.01 KB

Version

Bits

09f7f539

Nonce

158,366

Timestamp

11/16/2013, 9:25:53 PM

Confirmations

6,545,326

Mined by

⛏️ HaR^ANEJ2uT8T2Pi7Zn9LkcbWFnmeGYefcaoXo

Merkle Root

a078614ed5b2f0bd60637ddc9954031f758ca3ec452b925a76e9258756e3ab75

Transactions (1)

Coinbasea078614ed5b2f0…e9258756e3ab75

1 in → 56 out10.0300 XPM1.92 KB

ANEJ2uT8…YefcaoXo AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp

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.

6.604 × 10⁹¹(92-digit number)

66042305751636921726…62905086229984624719

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

6.604 × 10⁹¹(92-digit number)

66042305751636921726…62905086229984624719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.604 × 10⁹¹(92-digit number)

66042305751636921726…62905086229984624721

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

1.320 × 10⁹²(93-digit number)

13208461150327384345…25810172459969249439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.320 × 10⁹²(93-digit number)

13208461150327384345…25810172459969249441

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

2.641 × 10⁹²(93-digit number)

26416922300654768690…51620344919938498879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.641 × 10⁹²(93-digit number)

26416922300654768690…51620344919938498881

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

5.283 × 10⁹²(93-digit number)

52833844601309537381…03240689839876997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.283 × 10⁹²(93-digit number)

52833844601309537381…03240689839876997761

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

1.056 × 10⁹³(94-digit number)

10566768920261907476…06481379679753995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.056 × 10⁹³(94-digit number)

10566768920261907476…06481379679753995521

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 #262,472

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