Block #130,057

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/23/2013, 8:28:41 AM · Difficulty 9.7841 · 6,661,853 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94ff54918696746a57efaed7ba77ba16718f24d886554284a37aa095360a5e69

View on Chainz ↗

Height

#130,057

Difficulty

9.784086

Transactions

Size

202 B

Version

Bits

09c8b9e4

Nonce

75,399

Timestamp

8/23/2013, 8:28:41 AM

Confirmations

6,661,853

Merkle Root

8e6555afe219a6aca4c8d6ee0506ea14a8e5d27a0a1f94aa448b0ce458e4f0c2

Transactions (1)

Coinbase8e6555afe219a6…8b0ce458e4f0c2

1 in → 1 out10.4300 XPM109 B

ARjqnoYd…FsP3c6ZD

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.

6.300 × 10¹⁰¹(102-digit number)

63001063508525313888…26201385229738585319

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

6.300 × 10¹⁰¹(102-digit number)

63001063508525313888…26201385229738585319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.300 × 10¹⁰¹(102-digit number)

63001063508525313888…26201385229738585321

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

1.260 × 10¹⁰²(103-digit number)

12600212701705062777…52402770459477170639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.260 × 10¹⁰²(103-digit number)

12600212701705062777…52402770459477170641

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

2.520 × 10¹⁰²(103-digit number)

25200425403410125555…04805540918954341279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.520 × 10¹⁰²(103-digit number)

25200425403410125555…04805540918954341281

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

5.040 × 10¹⁰²(103-digit number)

50400850806820251110…09611081837908682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.040 × 10¹⁰²(103-digit number)

50400850806820251110…09611081837908682561

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

1.008 × 10¹⁰³(104-digit number)

10080170161364050222…19222163675817365119

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