Block #255,970

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 1:23:12 PM · Difficulty 9.9749 · 6,547,598 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

619346dd412091435d0bc08efcf03f30d6c3e6ce833d6d1afef37e10bbcd822f

View on Chainz ↗

Height

#255,970

Difficulty

9.974923

Transactions

Size

1.68 KB

Version

Bits

09f9948c

Nonce

307,589

Timestamp

11/11/2013, 1:23:12 PM

Confirmations

6,547,598

Mined by

⛏️ aRAQDGVS66x4YUbhY3Z3fTFJcuAE1PTWdWkm

Merkle Root

385a43c0fd9bb75e9703c046a972d12b04fe90390e86d2e00a69dd5f8ced683c

Transactions (1)

Coinbase385a43c0fd9bb7…69dd5f8ced683c

1 in → 46 out10.0200 XPM1.59 KB

AQDGVS66…1PTWdWkm AFqKfjez…qX9Ace3g ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY

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.

1.283 × 10⁹⁷(98-digit number)

12839812806515045790…73979074638993111039

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

1.283 × 10⁹⁷(98-digit number)

12839812806515045790…73979074638993111039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.283 × 10⁹⁷(98-digit number)

12839812806515045790…73979074638993111041

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

2.567 × 10⁹⁷(98-digit number)

25679625613030091581…47958149277986222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.567 × 10⁹⁷(98-digit number)

25679625613030091581…47958149277986222081

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

5.135 × 10⁹⁷(98-digit number)

51359251226060183163…95916298555972444159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.135 × 10⁹⁷(98-digit number)

51359251226060183163…95916298555972444161

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

1.027 × 10⁹⁸(99-digit number)

10271850245212036632…91832597111944888319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.027 × 10⁹⁸(99-digit number)

10271850245212036632…91832597111944888321

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

2.054 × 10⁹⁸(99-digit number)

20543700490424073265…83665194223889776639

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