Block #131,741

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/24/2013, 11:58:24 AM · Difficulty 9.7856 · 6,663,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b207623af231310b535401da9a917cd97dca33a58a244b861528c3ff8bfc7ae6

View on Chainz ↗

Height

#131,741

Difficulty

9.785587

Transactions

Size

1.18 KB

Version

Bits

09c91c43

Nonce

12,359

Timestamp

8/24/2013, 11:58:24 AM

Confirmations

6,663,137

Mined by

⛏️ P2SHAa398NxKwLMUZetUZxHnjpQrK8ypKhGVca

Merkle Root

3dbe6d464b6dd0d87d506af958e7b007fcfd62cf5ab737a245d6f5750d66e0cb

Transactions (3)

Coinbasee36948f0691c5b…266739dbabba43

1 in → 1 out10.4500 XPM109 B

Aa398NxK…ypKhGVca

a752bff978def7…d6587dfc06211d

5 in → 2 out1221.4933 XPM819 B

AY6ZehXo…5X1Appoz AJe8ACFo…TvcjAT89

5bbd9465542d5b…3d7881c9ebdcc3

1 in → 2 out10.4200 XPM193 B

AdxnvSqU…KQUw387u AGZvBxxa…shhkwtTn

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.

3.049 × 10⁹⁹(100-digit number)

30493870955379054242…06673415997153031749

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

3.049 × 10⁹⁹(100-digit number)

30493870955379054242…06673415997153031749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.049 × 10⁹⁹(100-digit number)

30493870955379054242…06673415997153031751

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

6.098 × 10⁹⁹(100-digit number)

60987741910758108484…13346831994306063499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.098 × 10⁹⁹(100-digit number)

60987741910758108484…13346831994306063501

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

1.219 × 10¹⁰⁰(101-digit number)

12197548382151621696…26693663988612126999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.219 × 10¹⁰⁰(101-digit number)

12197548382151621696…26693663988612127001

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

2.439 × 10¹⁰⁰(101-digit number)

24395096764303243393…53387327977224253999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.439 × 10¹⁰⁰(101-digit number)

24395096764303243393…53387327977224254001

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

4.879 × 10¹⁰⁰(101-digit number)

48790193528606486787…06774655954448507999

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