Block #2,942,662

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/28/2018, 6:55:22 AM · Difficulty 11.3940 · 3,891,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

885969e75061bbd5f9e304ecf4845976427b09e588acc3a75ca5644f040c4e5e

View on Chainz ↗

Height

#2,942,662

Difficulty

11.393969

Transactions

Size

1.95 KB

Version

Bits

0b64db2a

Nonce

1,131,947,953

Timestamp

11/28/2018, 6:55:22 AM

Confirmations

3,891,233

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

3496789715f07547876d9bbaf5fcb9c1c82bb7fa92bde59ba691d6381a30e62c

Transactions (5)

Coinbase9ccbacc984bca3…20979d822bb52a

1 in → 1 out7.7400 XPM110 B

AUhjokok…k5m93PZR

d09cb11d2ff5ce…5ecadf12092f09

5 in → 2 out4391.2434 XPM820 B

AcbKhjo3…JCMSWBDq ARywRRZa…HVd3P31R

c3781a2293c4d2…9b74549f8ca5bd

1 in → 2 out6.6894 XPM225 B

AbXwmGxD…4XXYP765 ATDtsKQ1…AbSZSoe4

e5cf03e3388494…e6cf310d771396

2 in → 2 out5.1966 XPM375 B

AKanrQFV…vieTTsaC AbXwmGxD…4XXYP765

5ef9fcbf93651c…4cb3bfce39bdb5

2 in → 2 out4.2353 XPM374 B

AbXwmGxD…4XXYP765 AK7gTG1e…nDmgCzsN

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.

3.012 × 10⁹⁸(99-digit number)

30120285694557042987…26365657371222343679

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

3.012 × 10⁹⁸(99-digit number)

30120285694557042987…26365657371222343679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.012 × 10⁹⁸(99-digit number)

30120285694557042987…26365657371222343681

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

6.024 × 10⁹⁸(99-digit number)

60240571389114085974…52731314742444687359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.024 × 10⁹⁸(99-digit number)

60240571389114085974…52731314742444687361

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

1.204 × 10⁹⁹(100-digit number)

12048114277822817194…05462629484889374719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.204 × 10⁹⁹(100-digit number)

12048114277822817194…05462629484889374721

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

2.409 × 10⁹⁹(100-digit number)

24096228555645634389…10925258969778749439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.409 × 10⁹⁹(100-digit number)

24096228555645634389…10925258969778749441

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

4.819 × 10⁹⁹(100-digit number)

48192457111291268779…21850517939557498879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.819 × 10⁹⁹(100-digit number)

48192457111291268779…21850517939557498881

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

9.638 × 10⁹⁹(100-digit number)

96384914222582537558…43701035879114997759

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 #2,942,662

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