Block #259,676

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 6:08:12 PM · Difficulty 9.9776 · 6,549,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0f8cb3b8015144a0b49660683c4dcb5ada051332de2e10f4ddb2223e1341913

View on Chainz ↗

Height

#259,676

Difficulty

9.977586

Transactions

Size

5.86 KB

Version

Bits

09fa430d

Nonce

14,162

Timestamp

11/13/2013, 6:08:12 PM

Confirmations

6,549,900

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

6488f4eb92fbe150153af8cbc05d4404f015d69cfcd1ab3a3f423e3434d5d458

Transactions (4)

Coinbasefbdb58e311b4bb…fb5df8a7daa0cb

1 in → 2 out10.1000 XPM136 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

f0f3e71b3169e8…ac26d754adbf3e

1 in → 2 out104.3507 XPM225 B

AZdmkNt9…Dk8ffFeU AM9wYqkJ…2YzSpWzP

771ec937578ace…ead2071247ab9b

3 in → 6 out20.6059 XPM589 B

AKLi48U1…7vwUf74K AUonD7JJ…MMmVvg91 ANWcCA1W…FYxSHbqJ AcADmAoe…8iNnoMzB AMuPGPXT…eMMNvd8v

0eb5aa0c7b04a0…912d2e45199384

33 in → 2 out200.0100 XPM4.84 KB

AHjZTj3i…e4Xho7yL AYoZxm5y…KqBr4mLv

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.

2.042 × 10⁹⁵(96-digit number)

20424209557456537519…81506135582522107519

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

2.042 × 10⁹⁵(96-digit number)

20424209557456537519…81506135582522107519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.042 × 10⁹⁵(96-digit number)

20424209557456537519…81506135582522107521

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

4.084 × 10⁹⁵(96-digit number)

40848419114913075039…63012271165044215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.084 × 10⁹⁵(96-digit number)

40848419114913075039…63012271165044215041

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

8.169 × 10⁹⁵(96-digit number)

81696838229826150078…26024542330088430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.169 × 10⁹⁵(96-digit number)

81696838229826150078…26024542330088430081

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

1.633 × 10⁹⁶(97-digit number)

16339367645965230015…52049084660176860159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.633 × 10⁹⁶(97-digit number)

16339367645965230015…52049084660176860161

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

3.267 × 10⁹⁶(97-digit number)

32678735291930460031…04098169320353720319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.267 × 10⁹⁶(97-digit number)

32678735291930460031…04098169320353720321

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 #259,676

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