Block #268,259

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2013, 11:38:20 PM · Difficulty 9.9576 · 6,549,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

980ccf862a143ee262dd247ba2b703230e0dd68459aab916fd6dc48f550439b8

View on Chainz ↗

Height

#268,259

Difficulty

9.957566

Transactions

Size

1.94 KB

Version

Bits

09f5230f

Nonce

43,067

Timestamp

11/21/2013, 11:38:20 PM

Confirmations

6,549,289

Mined by

⛏️ aRAMttQDuftdpMyrb199TXiUSH5L7j6tfS9x

Merkle Root

96a987967a72c283a200f12de8db3db02fa76c39ca62b91b3dd6d074e71b4e8c

Transactions (1)

Coinbase96a987967a72c2…d6d074e71b4e8c

1 in → 54 out10.0500 XPM1.85 KB

AMttQDuf…7j6tfS9x AFqKfjez…qX9Ace3g ANuKx9Ke…wm7nrBRq APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs

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.

5.179 × 10⁹⁵(96-digit number)

51793303868396412981…55787504555306065919

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

5.179 × 10⁹⁵(96-digit number)

51793303868396412981…55787504555306065919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.179 × 10⁹⁵(96-digit number)

51793303868396412981…55787504555306065921

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

1.035 × 10⁹⁶(97-digit number)

10358660773679282596…11575009110612131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.035 × 10⁹⁶(97-digit number)

10358660773679282596…11575009110612131841

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

2.071 × 10⁹⁶(97-digit number)

20717321547358565192…23150018221224263679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.071 × 10⁹⁶(97-digit number)

20717321547358565192…23150018221224263681

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

4.143 × 10⁹⁶(97-digit number)

41434643094717130384…46300036442448527359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.143 × 10⁹⁶(97-digit number)

41434643094717130384…46300036442448527361

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

8.286 × 10⁹⁶(97-digit number)

82869286189434260769…92600072884897054719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.286 × 10⁹⁶(97-digit number)

82869286189434260769…92600072884897054721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.657 × 10⁹⁷(98-digit number)

16573857237886852153…85200145769794109439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #268,259

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