Block #291,888

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 10:34:17 AM · Difficulty 9.9901 · 6,516,531 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbc071923cf5a74f80deb9d4b08a19d36904a0ff2d8195b455629f3d4eef15b3

View on Chainz ↗

Height

#291,888

Difficulty

9.990059

Transactions

Size

832 B

Version

Bits

09fd7480

Nonce

500,544

Timestamp

12/3/2013, 10:34:17 AM

Confirmations

6,516,531

Mined by

⛏️ 0taR?APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

37f4a8872b1dfb00b7387868e62069d3295957f9a2a01ea2cf77d198d06a6c36

Transactions (1)

Coinbase37f4a8872b1dfb…77d198d06a6c36

1 in → 20 out10.0000 XPM743 B

APeshfYV…3PKcKMKH Ad9pSzHt…cpJ3y2zz AZninDSu…FvgDMwC4 ARzXge7S…CEjL5oYm AYxtkmef…SXCx2bKi

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.

2.906 × 10⁹³(94-digit number)

29061264578041933084…66278774651330096039

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

2.906 × 10⁹³(94-digit number)

29061264578041933084…66278774651330096039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.906 × 10⁹³(94-digit number)

29061264578041933084…66278774651330096041

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

5.812 × 10⁹³(94-digit number)

58122529156083866169…32557549302660192079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.812 × 10⁹³(94-digit number)

58122529156083866169…32557549302660192081

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

1.162 × 10⁹⁴(95-digit number)

11624505831216773233…65115098605320384159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.162 × 10⁹⁴(95-digit number)

11624505831216773233…65115098605320384161

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

2.324 × 10⁹⁴(95-digit number)

23249011662433546467…30230197210640768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.324 × 10⁹⁴(95-digit number)

23249011662433546467…30230197210640768321

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

4.649 × 10⁹⁴(95-digit number)

46498023324867092935…60460394421281536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.649 × 10⁹⁴(95-digit number)

46498023324867092935…60460394421281536641

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 #291,888

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