Block #130,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/23/2013, 10:47:22 AM · Difficulty 9.7841 · 6,675,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f17f1e77c114be9293ebac3de9af4ac042b2d1de00589a11907814ddea1188d1

View on Chainz ↗

Height

#130,197

Difficulty

9.784119

Transactions

Size

395 B

Version

Bits

09c8bc06

Nonce

10,408

Timestamp

8/23/2013, 10:47:22 AM

Confirmations

6,675,076

Mined by

⛏️ P2SHAWbAeqNJW2hke79Loy2hRg6rqcox13tJA2

Merkle Root

7773708b72bc90d4ddf0007c6d109d094d9bbf91d8eb8e269f9c1d5e5c5fa8c2

Transactions (2)

Coinbase482d0ec79f013e…e114e1cb91fdf6

1 in → 1 out10.4400 XPM109 B

AWbAeqNJ…ox13tJA2

e124f1066c0b18…4b14904b4bd551

1 in → 1 out42.2800 XPM192 B

AKVZmjFY…iuD64V6a

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.

3.813 × 10¹⁰³(104-digit number)

38139812733107404192…12330579281227831149

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

3.813 × 10¹⁰³(104-digit number)

38139812733107404192…12330579281227831149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.813 × 10¹⁰³(104-digit number)

38139812733107404192…12330579281227831151

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

7.627 × 10¹⁰³(104-digit number)

76279625466214808384…24661158562455662299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.627 × 10¹⁰³(104-digit number)

76279625466214808384…24661158562455662301

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

1.525 × 10¹⁰⁴(105-digit number)

15255925093242961676…49322317124911324599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.525 × 10¹⁰⁴(105-digit number)

15255925093242961676…49322317124911324601

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

3.051 × 10¹⁰⁴(105-digit number)

30511850186485923353…98644634249822649199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.051 × 10¹⁰⁴(105-digit number)

30511850186485923353…98644634249822649201

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

6.102 × 10¹⁰⁴(105-digit number)

61023700372971846707…97289268499645298399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.102 × 10¹⁰⁴(105-digit number)

61023700372971846707…97289268499645298401

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