Block #1,456,144

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/14/2016, 11:19:51 AM · Difficulty 10.7411 · 5,361,684 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae3b069191a72969ea3aad9b23963017013aff927d763195b026c87e0ec26bab

View on Chainz ↗

Height

#1,456,144

Difficulty

10.741146

Transactions

Size

5.61 KB

Version

Bits

0abdbbc1

Nonce

409,346,566

Timestamp

2/14/2016, 11:19:51 AM

Confirmations

5,361,684

Mined by

⛏️ P2SHAcHXbWDfCKKz2wouQ8AbT9pkdBj65t7E3F

Merkle Root

6e5db0904aa606e007dfc137eb52ec3f801c285a3c96e7700333620ed183d36e

Transactions (2)

Coinbase585ea4822e173c…928999edda8941

1 in → 1 out8.8000 XPM109 B

AcHXbWDf…j65t7E3F

25e41790a72ee7…f9a3c7cc5b9c6e

37 in → 2 out333.6800 XPM5.41 KB

AcDhjHA9…ebukETHz ANCiaaZJ…g9zHDKsf

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.

1.797 × 10⁹⁵(96-digit number)

17972556929843501237…96963799076135550719

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

1.797 × 10⁹⁵(96-digit number)

17972556929843501237…96963799076135550719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.797 × 10⁹⁵(96-digit number)

17972556929843501237…96963799076135550721

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

3.594 × 10⁹⁵(96-digit number)

35945113859687002474…93927598152271101439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.594 × 10⁹⁵(96-digit number)

35945113859687002474…93927598152271101441

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

7.189 × 10⁹⁵(96-digit number)

71890227719374004948…87855196304542202879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.189 × 10⁹⁵(96-digit number)

71890227719374004948…87855196304542202881

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

1.437 × 10⁹⁶(97-digit number)

14378045543874800989…75710392609084405759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.437 × 10⁹⁶(97-digit number)

14378045543874800989…75710392609084405761

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

2.875 × 10⁹⁶(97-digit number)

28756091087749601979…51420785218168811519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.875 × 10⁹⁶(97-digit number)

28756091087749601979…51420785218168811521

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

5.751 × 10⁹⁶(97-digit number)

57512182175499203958…02841570436337623039

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 #1,456,144

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