Block #286,611

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 11:26:02 PM · Difficulty 9.9858 · 6,523,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b2c14ac33b6c527888682bd7991d9a69f427c4955e0bd287ec8bf0193a513e0

View on Chainz ↗

Height

#286,611

Difficulty

9.985777

Transactions

Size

1.18 KB

Version

Bits

09fc5be1

Nonce

48,333

Timestamp

11/30/2013, 11:26:02 PM

Confirmations

6,523,286

Mined by

⛏️ _aRt_AVKFC9nD3snNraYcHrou5F67vCJ9zTymTX

Merkle Root

ed7f0f759576a69a390a47eff75be797517957a6cd7a2ed382b8295f370f3635

Transactions (1)

Coinbaseed7f0f759576a6…b8295f370f3635

1 in → 31 out9.9900 XPM1.09 KB

AVKFC9nD…J9zTymTX AXz2kWvX…V5ZFCDBd AVBfQUgC…NWHsLqSF Ad9pSzHt…cpJ3y2zz AT5YHFNE…wEB3sX3V

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.

4.251 × 10⁹¹(92-digit number)

42516336995891698803…62565665652286848799

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

4.251 × 10⁹¹(92-digit number)

42516336995891698803…62565665652286848799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.251 × 10⁹¹(92-digit number)

42516336995891698803…62565665652286848801

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

8.503 × 10⁹¹(92-digit number)

85032673991783397607…25131331304573697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.503 × 10⁹¹(92-digit number)

85032673991783397607…25131331304573697601

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

1.700 × 10⁹²(93-digit number)

17006534798356679521…50262662609147395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.700 × 10⁹²(93-digit number)

17006534798356679521…50262662609147395201

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

3.401 × 10⁹²(93-digit number)

34013069596713359042…00525325218294790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.401 × 10⁹²(93-digit number)

34013069596713359042…00525325218294790401

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

6.802 × 10⁹²(93-digit number)

68026139193426718085…01050650436589580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.802 × 10⁹²(93-digit number)

68026139193426718085…01050650436589580801

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 #286,611

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