Block #243,277

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 5:08:32 AM · Difficulty 9.9613 · 6,587,868 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

781f52a14eeef2bd2a5afc3f45544f13ad7dc6379ca96a6a9a704b6b77bb729e

View on Chainz ↗

Height

#243,277

Difficulty

9.961262

Transactions

Size

1.78 KB

Version

Bits

09f61542

Nonce

182,405

Timestamp

11/4/2013, 5:08:32 AM

Confirmations

6,587,868

Mined by

⛏️ MRw+AdWEcK3rEzi97mdrbQ1dKgt3GmHNaeWgVb

Merkle Root

de659e88781d8c401d049a146b54762a9987d509c951f6f60c4ca793828869e4

Transactions (1)

Coinbasede659e88781d8c…4ca793828869e4

1 in → 49 out10.0400 XPM1.69 KB

AdWEcK3r…HNaeWgVb AabHNb1B…GRoingRy ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ALSiuDiS…WqQxGQSY

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.

1.283 × 10⁹⁵(96-digit number)

12838118810307963095…43781782294553515519

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

1.283 × 10⁹⁵(96-digit number)

12838118810307963095…43781782294553515519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.283 × 10⁹⁵(96-digit number)

12838118810307963095…43781782294553515521

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

2.567 × 10⁹⁵(96-digit number)

25676237620615926190…87563564589107031039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.567 × 10⁹⁵(96-digit number)

25676237620615926190…87563564589107031041

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

5.135 × 10⁹⁵(96-digit number)

51352475241231852380…75127129178214062079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.135 × 10⁹⁵(96-digit number)

51352475241231852380…75127129178214062081

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

1.027 × 10⁹⁶(97-digit number)

10270495048246370476…50254258356428124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10270495048246370476…50254258356428124161

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

2.054 × 10⁹⁶(97-digit number)

20540990096492740952…00508516712856248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.054 × 10⁹⁶(97-digit number)

20540990096492740952…00508516712856248321

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 #243,277

Cookie Preferences