Block #282,019

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 6:00:28 AM · Difficulty 9.9782 · 6,561,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ff684e059f9b97433ce0a2be28dab0cada1da534a4e6a129ed24430be432285

View on Chainz ↗

Height

#282,019

Difficulty

9.978220

Transactions

Size

1.18 KB

Version

Bits

09fa6ca1

Nonce

103,238

Timestamp

11/29/2013, 6:00:28 AM

Confirmations

6,561,372

Mined by

⛏️ MaR-cAbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

1abc7cfa0158ca33c0f14c0e26a96a1448ff8b7d9ef3d07f8452250ef8593c93

Transactions (1)

Coinbase1abc7cfa0158ca…52250ef8593c93

1 in → 31 out10.0100 XPM1.09 KB

AbtgNzNb…9Atvu81w Ad9pSzHt…cpJ3y2zz AZFzn5KH…oHfafeEn AP5UvYhU…vLTDwkdA AXALnvoH…GreXAjNF

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.

1.550 × 10⁹⁵(96-digit number)

15500083554431453734…17153760098864803199

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

1.550 × 10⁹⁵(96-digit number)

15500083554431453734…17153760098864803199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.550 × 10⁹⁵(96-digit number)

15500083554431453734…17153760098864803201

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

3.100 × 10⁹⁵(96-digit number)

31000167108862907469…34307520197729606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.100 × 10⁹⁵(96-digit number)

31000167108862907469…34307520197729606401

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

6.200 × 10⁹⁵(96-digit number)

62000334217725814938…68615040395459212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.200 × 10⁹⁵(96-digit number)

62000334217725814938…68615040395459212801

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

1.240 × 10⁹⁶(97-digit number)

12400066843545162987…37230080790918425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.240 × 10⁹⁶(97-digit number)

12400066843545162987…37230080790918425601

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

2.480 × 10⁹⁶(97-digit number)

24800133687090325975…74460161581836851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.480 × 10⁹⁶(97-digit number)

24800133687090325975…74460161581836851201

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 #282,019

Cookie Preferences