Block #29,895

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 5:06:21 PM · Difficulty 7.9857 · 6,764,499 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

245487833aa2c3765954f4bc108b2c6f89ad394e07d722e00ad342eeba78f26f

View on Chainz ↗

Height

#29,895

Difficulty

7.985702

Transactions

Size

726 B

Version

Bits

07fc56fa

Nonce

917

Timestamp

7/13/2013, 5:06:21 PM

Confirmations

6,764,499

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

e70edaadd07430f4ab26d7e7d17f87424c97fe14f04b89a95a242e279a175b13

Transactions (2)

Coinbase17c1f2064e26ba…1502a93fe9acab

1 in → 1 out15.6700 XPM108 B

AKSwr9eU…dLNxuVyn

da3474772ca180…37b7c1246a30a3

3 in → 2 out154.8500 XPM522 B

AK5ihq28…YRTMK7RU AUnc2ttj…7VricqLj

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.

3.905 × 10¹⁰⁸(109-digit number)

39050725278021994598…74864881028992985609

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

3.905 × 10¹⁰⁸(109-digit number)

39050725278021994598…74864881028992985609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.905 × 10¹⁰⁸(109-digit number)

39050725278021994598…74864881028992985611

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

7.810 × 10¹⁰⁸(109-digit number)

78101450556043989197…49729762057985971219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.810 × 10¹⁰⁸(109-digit number)

78101450556043989197…49729762057985971221

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

1.562 × 10¹⁰⁹(110-digit number)

15620290111208797839…99459524115971942439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.562 × 10¹⁰⁹(110-digit number)

15620290111208797839…99459524115971942441

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

3.124 × 10¹⁰⁹(110-digit number)

31240580222417595678…98919048231943884879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.124 × 10¹⁰⁹(110-digit number)

31240580222417595678…98919048231943884881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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