Block #135,267

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 12:49:25 PM · Difficulty 9.8096 · 6,668,968 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

760bd9efc050c34e53a376d5877db8205aacc868406918824dc33c0cd51e4669

View on Chainz ↗

Height

#135,267

Difficulty

9.809596

Transactions

Size

582 B

Version

Bits

09cf41b7

Nonce

119,523

Timestamp

8/26/2013, 12:49:25 PM

Confirmations

6,668,968

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

d8dce9fdd75ec310f601ed3a145e5c8f4d32ec61891af6c966640ed5b0c90acf

Transactions (3)

Coinbase80d079b8f1fbaf…efb84ca7f32d89

1 in → 1 out10.4000 XPM109 B

Acecj4WY…wKtCNbS5

15c0d80f365808…85155f0af52d09

1 in → 2 out10.4400 XPM192 B

AaMRUFMG…S11BNFrC APVSSVUM…izt9kCEZ

bd81d4a79c8775…6cda091346d35c

1 in → 1 out5.2150 XPM193 B

AeguK5Ai…CLUqoF9q

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.

4.677 × 10⁹⁰(91-digit number)

46777698950249145019…34797992462695922099

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

4.677 × 10⁹⁰(91-digit number)

46777698950249145019…34797992462695922099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.677 × 10⁹⁰(91-digit number)

46777698950249145019…34797992462695922101

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

9.355 × 10⁹⁰(91-digit number)

93555397900498290038…69595984925391844199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.355 × 10⁹⁰(91-digit number)

93555397900498290038…69595984925391844201

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

1.871 × 10⁹¹(92-digit number)

18711079580099658007…39191969850783688399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.871 × 10⁹¹(92-digit number)

18711079580099658007…39191969850783688401

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

3.742 × 10⁹¹(92-digit number)

37422159160199316015…78383939701567376799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.742 × 10⁹¹(92-digit number)

37422159160199316015…78383939701567376801

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

7.484 × 10⁹¹(92-digit number)

74844318320398632030…56767879403134753599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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