Block #268,349

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 1:39:31 AM · Difficulty 9.9573 · 6,526,503 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2de92a39c940a68931a5d640e2517ffd79b7847476b587ac0a9d21848f5bf74

View on Chainz ↗

Height

#268,349

Difficulty

9.957314

Transactions

Size

945 B

Version

Bits

09f51287

Nonce

25,320

Timestamp

11/22/2013, 1:39:31 AM

Confirmations

6,526,503

Mined by

⛏️ P2SHAUPwX3FPEiWJ6GajdLzRS48aBtb2mxFeSt

Merkle Root

163c396aeaa8ca9bf4c2788699e799fce69d39ef07b907f097bd2c524afc5e0d

Transactions (3)

Coinbase24294e17885d82…dce93e1dabeb69

1 in → 1 out10.0900 XPM109 B

AUPwX3FP…b2mxFeSt

343505a317d8b1…86d9159f8133d2

2 in → 2 out702.9900 XPM375 B

AJFejZX3…Cat9VRow ALgtM2MK…scrMYgnx

e64fb2ec5468ad…0c2873692c6739

2 in → 2 out109.2595 XPM372 B

AX65w2u1…U9FMmnRi AJjBJEpS…yxANCh2L

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.

2.581 × 10⁹³(94-digit number)

25813097613935119577…05528659818333281279

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

2.581 × 10⁹³(94-digit number)

25813097613935119577…05528659818333281279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.581 × 10⁹³(94-digit number)

25813097613935119577…05528659818333281281

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

5.162 × 10⁹³(94-digit number)

51626195227870239155…11057319636666562559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.162 × 10⁹³(94-digit number)

51626195227870239155…11057319636666562561

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

1.032 × 10⁹⁴(95-digit number)

10325239045574047831…22114639273333125119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.032 × 10⁹⁴(95-digit number)

10325239045574047831…22114639273333125121

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

2.065 × 10⁹⁴(95-digit number)

20650478091148095662…44229278546666250239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.065 × 10⁹⁴(95-digit number)

20650478091148095662…44229278546666250241

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

4.130 × 10⁹⁴(95-digit number)

41300956182296191324…88458557093332500479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.130 × 10⁹⁴(95-digit number)

41300956182296191324…88458557093332500481

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