Block #281,747

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 3:34:49 AM · Difficulty 9.9777 · 6,544,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40aa3661c41cdc1cddfaf30e9d429082344e4a08d45277c69d2ce489e8a24792

View on Chainz ↗

Height

#281,747

Difficulty

9.977659

Transactions

Size

1.01 KB

Version

Bits

09fa47d7

Nonce

218,752

Timestamp

11/29/2013, 3:34:49 AM

Confirmations

6,544,828

Mined by

⛏️ LaR>zAWGQhzDNqt1A9FGXDdvgYQjDXoRDYvugUy

Merkle Root

b03be957bf373f1b90f4e04d1b5ef80a81342e74fb84e3b6fd7ee4385adf00af

Transactions (1)

Coinbaseb03be957bf373f…7ee4385adf00af

1 in → 26 out10.0300 XPM947 B

AWGQhzDN…RDYvugUy AGFAJ5YL…ZEnBbk6G AYrgZtF4…6oLCC7XK AG8UzQTL…AeALjTXg Ad9pSzHt…cpJ3y2zz

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.

1.944 × 10⁹³(94-digit number)

19444967738400960457…10176031688347212799

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

1.944 × 10⁹³(94-digit number)

19444967738400960457…10176031688347212799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.944 × 10⁹³(94-digit number)

19444967738400960457…10176031688347212801

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

3.888 × 10⁹³(94-digit number)

38889935476801920915…20352063376694425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.888 × 10⁹³(94-digit number)

38889935476801920915…20352063376694425601

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

7.777 × 10⁹³(94-digit number)

77779870953603841830…40704126753388851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.777 × 10⁹³(94-digit number)

77779870953603841830…40704126753388851201

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

1.555 × 10⁹⁴(95-digit number)

15555974190720768366…81408253506777702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.555 × 10⁹⁴(95-digit number)

15555974190720768366…81408253506777702401

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

3.111 × 10⁹⁴(95-digit number)

31111948381441536732…62816507013555404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.111 × 10⁹⁴(95-digit number)

31111948381441536732…62816507013555404801

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 #281,747

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