Block #276,840

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 8:28:51 AM · Difficulty 9.9644 · 6,540,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dcdb7b6487e7da0bf9e6a9168eda0c15dba8319cc2bbca596eaf12a7c8513d96

View on Chainz ↗

Height

#276,840

Difficulty

9.964394

Transactions

Size

1.15 KB

Version

Bits

09f6e281

Nonce

166,953

Timestamp

11/27/2013, 8:28:51 AM

Confirmations

6,540,289

Mined by

⛏️ h9aR-qAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

c6f538808e3abfb7c274f3d3140ad8796092a7f827e2489dcf60cb94a822055b

Transactions (1)

Coinbasec6f538808e3abf…60cb94a822055b

1 in → 30 out10.0400 XPM1.06 KB

APeshfYV…3PKcKMKH AScAzqGc…BZ6tV1vJ Abv8pzf1…t4zPXDTV AWGQhzDN…RDYvugUy AKFexj5z…6S5VHRVy

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.

5.523 × 10⁹⁷(98-digit number)

55235506344910963253…98084254409502701119

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

5.523 × 10⁹⁷(98-digit number)

55235506344910963253…98084254409502701119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.523 × 10⁹⁷(98-digit number)

55235506344910963253…98084254409502701121

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

1.104 × 10⁹⁸(99-digit number)

11047101268982192650…96168508819005402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.104 × 10⁹⁸(99-digit number)

11047101268982192650…96168508819005402241

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

2.209 × 10⁹⁸(99-digit number)

22094202537964385301…92337017638010804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.209 × 10⁹⁸(99-digit number)

22094202537964385301…92337017638010804481

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

4.418 × 10⁹⁸(99-digit number)

44188405075928770603…84674035276021608959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.418 × 10⁹⁸(99-digit number)

44188405075928770603…84674035276021608961

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

8.837 × 10⁹⁸(99-digit number)

88376810151857541206…69348070552043217919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.837 × 10⁹⁸(99-digit number)

88376810151857541206…69348070552043217921

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 #276,840

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