Block #286,914

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 2:28:23 AM · Difficulty 9.9861 · 6,512,115 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25f069b46c7e3ce431dae47b69fe21dfb953d32762ff754faa38132eace00324

View on Chainz ↗

Height

#286,914

Difficulty

9.986121

Transactions

Size

801 B

Version

Bits

09fc7266

Nonce

3,907

Timestamp

12/1/2013, 2:28:23 AM

Confirmations

6,512,115

Mined by

⛏️ P2SHAKUGamHqURk3qLCjvfDZQmrqQgPTwGDuor

Merkle Root

c1e43d7b66721c9504ee082b9a0845d22d50d7574536f8fae972edf5a54f05c5

Transactions (3)

Coinbase56f8be1c0d8d5b…f05d954a812cef

1 in → 1 out10.0300 XPM109 B

AKUGamHq…PTwGDuor

8913b1c66bb6f6…0227ce3b3a1989

1 in → 2 out2258.9800 XPM226 B

AQjJPJRN…xG8ABQ4W AcbFiMvX…E85VcHeN

6f08ddebfd646a…023dcbb986cea7

2 in → 2 out160.6377 XPM375 B

AQnesyRk…uyJiHpPC AcK2HALC…YEooUj8S

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.

5.534 × 10⁹⁶(97-digit number)

55349323315266762995…95577426083957206399

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

5.534 × 10⁹⁶(97-digit number)

55349323315266762995…95577426083957206399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.534 × 10⁹⁶(97-digit number)

55349323315266762995…95577426083957206401

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

1.106 × 10⁹⁷(98-digit number)

11069864663053352599…91154852167914412799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.106 × 10⁹⁷(98-digit number)

11069864663053352599…91154852167914412801

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

2.213 × 10⁹⁷(98-digit number)

22139729326106705198…82309704335828825599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.213 × 10⁹⁷(98-digit number)

22139729326106705198…82309704335828825601

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

4.427 × 10⁹⁷(98-digit number)

44279458652213410396…64619408671657651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.427 × 10⁹⁷(98-digit number)

44279458652213410396…64619408671657651201

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

8.855 × 10⁹⁷(98-digit number)

88558917304426820792…29238817343315302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.855 × 10⁹⁷(98-digit number)

88558917304426820792…29238817343315302401

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