Block #892,147

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2015, 9:07:56 AM · Difficulty 10.9524 · 5,911,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b4db9e08d6b696064bdbc9310bfe88f3050f967dcf778041845a9b3717e03f4

View on Chainz ↗

Height

#892,147

Difficulty

10.952444

Transactions

Size

1.52 KB

Version

Bits

0af3d366

Nonce

2,252,061,640

Timestamp

1/12/2015, 9:07:56 AM

Confirmations

5,911,476

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f2ea495c487f6b56da5e75a998cd9b457288b7cd7e6b8bc6a4302df68509db6e

Transactions (5)

Coinbaseb8dfe52120395f…16b6ab29b0985e

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

54fc888991b6d9…83efcd8c06eade

1 in → 2 out8.3000 XPM227 B

ARo8ybTK…oYpPzn5U AMuYYsgd…ioD1TEUt

e1de36eb0b46e2…335acf3fc7b7a5

1 in → 2 out8.3000 XPM227 B

Ae7YXEyn…hnSYZsCr AcTpECyq…45ZxDPKc

bcde62f236f9ce…a743a7704bf578

1 in → 2 out7.1267 XPM226 B

ALP6szJY…eEPSo5sX AWPmUVhv…d3d8vvX5

36523e40547219…574406e9160a71

4 in → 2 out2.0974 XPM668 B

AHRoBSh4…BSVTQ36Q ATrqCHSo…mKVpVRxo

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.

5.890 × 10⁹³(94-digit number)

58907800630573073350…99422909694389573679

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

5.890 × 10⁹³(94-digit number)

58907800630573073350…99422909694389573679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.890 × 10⁹³(94-digit number)

58907800630573073350…99422909694389573681

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

1.178 × 10⁹⁴(95-digit number)

11781560126114614670…98845819388779147359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.178 × 10⁹⁴(95-digit number)

11781560126114614670…98845819388779147361

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

2.356 × 10⁹⁴(95-digit number)

23563120252229229340…97691638777558294719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.356 × 10⁹⁴(95-digit number)

23563120252229229340…97691638777558294721

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

4.712 × 10⁹⁴(95-digit number)

47126240504458458680…95383277555116589439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.712 × 10⁹⁴(95-digit number)

47126240504458458680…95383277555116589441

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

9.425 × 10⁹⁴(95-digit number)

94252481008916917361…90766555110233178879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.425 × 10⁹⁴(95-digit number)

94252481008916917361…90766555110233178881

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