Block #268,249

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 11:23:53 PM · Difficulty 9.9576 · 6,557,273 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf8db4ba2d0eb04d3ae5b2557a9fe8fda831c759731da2a72ff3c6d339848322

View on Chainz ↗

Height

#268,249

Difficulty

9.957599

Transactions

Size

1.84 KB

Version

Bits

09f52530

Nonce

367,826

Timestamp

11/21/2013, 11:23:53 PM

Confirmations

6,557,273

Mined by

⛏️ aRLATaiAP5CNeTYrcp775AJmapQ3Vo4tqgUvu

Merkle Root

924e3a0aa857b04afa6fccd20e8b9fc95be8789d79d93dbf38dcd73da0a8670f

Transactions (1)

Coinbase924e3a0aa857b0…dcd73da0a8670f

1 in → 51 out10.0500 XPM1.75 KB

ATaiAP5C…o4tqgUvu AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

2.440 × 10⁹¹(92-digit number)

24404093286517903194…41954894058002319359

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

2.440 × 10⁹¹(92-digit number)

24404093286517903194…41954894058002319359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.440 × 10⁹¹(92-digit number)

24404093286517903194…41954894058002319361

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

4.880 × 10⁹¹(92-digit number)

48808186573035806389…83909788116004638719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.880 × 10⁹¹(92-digit number)

48808186573035806389…83909788116004638721

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

9.761 × 10⁹¹(92-digit number)

97616373146071612778…67819576232009277439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.761 × 10⁹¹(92-digit number)

97616373146071612778…67819576232009277441

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

1.952 × 10⁹²(93-digit number)

19523274629214322555…35639152464018554879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.952 × 10⁹²(93-digit number)

19523274629214322555…35639152464018554881

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

3.904 × 10⁹²(93-digit number)

39046549258428645111…71278304928037109759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.904 × 10⁹²(93-digit number)

39046549258428645111…71278304928037109761

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 #268,249

Cookie Preferences