Block #265,261

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 9:54:12 AM · Difficulty 9.9630 · 6,528,926 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf6905147ffcf14c318000a745bb41ae52a8d09253a638ae9aeb0fced601fd31

View on Chainz ↗

Height

#265,261

Difficulty

9.963004

Transactions

Size

1.07 KB

Version

Bits

09f6876d

Nonce

18,069

Timestamp

11/19/2013, 9:54:12 AM

Confirmations

6,528,926

Merkle Root

5f73b75b5b1efdb909455bde46c3732434d95d5f4a35c8741e25003bd261a09c

Transactions (3)

Coinbase11cd5e5eee35a8…197db10d708cf1

1 in → 1 out10.0800 XPM109 B

AVgtscKT…NLH2Y5kN

87a211e1c70f79…c08d8c45e7c7ed

3 in → 2 out440.5292 XPM523 B

AeLo3idy…3UjxF275 AdvoZrcX…vwAo57ep

967785eb832f0b…f10c4420ab4d77

2 in → 2 out14.9100 XPM374 B

ALDMgCdh…WBic481T ANKaqdoT…rPahfJui

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.

1.792 × 10⁹²(93-digit number)

17922945723242828664…23909763836732646199

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

1.792 × 10⁹²(93-digit number)

17922945723242828664…23909763836732646199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.792 × 10⁹²(93-digit number)

17922945723242828664…23909763836732646201

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

3.584 × 10⁹²(93-digit number)

35845891446485657328…47819527673465292399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.584 × 10⁹²(93-digit number)

35845891446485657328…47819527673465292401

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

7.169 × 10⁹²(93-digit number)

71691782892971314657…95639055346930584799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.169 × 10⁹²(93-digit number)

71691782892971314657…95639055346930584801

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

1.433 × 10⁹³(94-digit number)

14338356578594262931…91278110693861169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.433 × 10⁹³(94-digit number)

14338356578594262931…91278110693861169601

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

2.867 × 10⁹³(94-digit number)

28676713157188525863…82556221387722339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.867 × 10⁹³(94-digit number)

28676713157188525863…82556221387722339201

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