Block #911,752

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2015, 8:41:22 AM · Difficulty 10.9305 · 5,895,207 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4ea13d9abb277ee54ad4b8f529517618dafdb40a4183c5c2eb252c10fe10246

View on Chainz ↗

Height

#911,752

Difficulty

10.930475

Transactions

Size

729 B

Version

Bits

0aee3397

Nonce

256,440,662

Timestamp

1/27/2015, 8:41:22 AM

Confirmations

5,895,207

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ad5f15389ab702bde3498ba407cb77b42489ad6547a2c717ea0c88cf7a5195bf

Transactions (2)

Coinbaseb466296716916f…ccde72186c9831

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

249c7a968a06ac…b09e670fd47f65

3 in → 2 out103.4457 XPM521 B

AMz4ubvV…X7KpRfoS ARoPpPjC…Ndoa3iQv

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.

7.830 × 10⁹⁸(99-digit number)

78304685941603450625…31049657834458972159

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

7.830 × 10⁹⁸(99-digit number)

78304685941603450625…31049657834458972159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.830 × 10⁹⁸(99-digit number)

78304685941603450625…31049657834458972161

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

1.566 × 10⁹⁹(100-digit number)

15660937188320690125…62099315668917944319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.566 × 10⁹⁹(100-digit number)

15660937188320690125…62099315668917944321

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

3.132 × 10⁹⁹(100-digit number)

31321874376641380250…24198631337835888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.132 × 10⁹⁹(100-digit number)

31321874376641380250…24198631337835888641

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

6.264 × 10⁹⁹(100-digit number)

62643748753282760500…48397262675671777279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.264 × 10⁹⁹(100-digit number)

62643748753282760500…48397262675671777281

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

1.252 × 10¹⁰⁰(101-digit number)

12528749750656552100…96794525351343554559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.252 × 10¹⁰⁰(101-digit number)

12528749750656552100…96794525351343554561

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 #911,752

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