Block #125,330

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/20/2013, 4:22:12 AM · Difficulty 9.7769 · 6,678,880 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b0ffb513ae7d36687d3e4bad7f457b04611040a04515a581cda68c261faa087

View on Chainz ↗

Height

#125,330

Difficulty

9.776924

Transactions

Size

1.42 KB

Version

Bits

09c6e478

Nonce

351,023

Timestamp

8/20/2013, 4:22:12 AM

Confirmations

6,678,880

Mined by

⛏️ P2SHAPEcDKBhiwmtCs4uPmnx1PYtaBbvmts2ty

Merkle Root

7562a78c4ac28f0745b930aa1f448527f034fe315b546c3e6613936aef63f1c7

Transactions (2)

Coinbase5b8508d32e74a6…75285802b6b824

1 in → 1 out10.4700 XPM109 B

APEcDKBh…bvmts2ty

f95be8b6e3f235…42a7ee16421d8c

10 in → 2 out95.2333 XPM1.23 KB

AV86XQsY…mweuCpSm AenF1rZa…Q9LffyKG

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.

7.764 × 10⁹⁹(100-digit number)

77641170969461940473…90156094715594057299

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

7.764 × 10⁹⁹(100-digit number)

77641170969461940473…90156094715594057299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.764 × 10⁹⁹(100-digit number)

77641170969461940473…90156094715594057301

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

1.552 × 10¹⁰⁰(101-digit number)

15528234193892388094…80312189431188114599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.552 × 10¹⁰⁰(101-digit number)

15528234193892388094…80312189431188114601

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

3.105 × 10¹⁰⁰(101-digit number)

31056468387784776189…60624378862376229199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.105 × 10¹⁰⁰(101-digit number)

31056468387784776189…60624378862376229201

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

6.211 × 10¹⁰⁰(101-digit number)

62112936775569552378…21248757724752458399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.211 × 10¹⁰⁰(101-digit number)

62112936775569552378…21248757724752458401

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

1.242 × 10¹⁰¹(102-digit number)

12422587355113910475…42497515449504916799

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