Block #26,111

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 4:20:05 AM · Difficulty 7.9738 · 6,763,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30a7fafbaa696aafb8defb8cc30bed0e1e80279c20c6da438f9df4188a52dcda

View on Chainz ↗

Height

#26,111

Difficulty

7.973825

Transactions

Size

197 B

Version

Bits

07f94c94

Nonce

185

Timestamp

7/13/2013, 4:20:05 AM

Confirmations

6,763,750

Merkle Root

73c6889965dd136908b4e7cf2551a3ac905d153f82ba9a062c7f5603ed3dd923

Transactions (1)

Coinbase73c6889965dd13…7f5603ed3dd923

1 in → 1 out15.7100 XPM108 B

ARGeTm8M…CBEPy9T2

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.

3.971 × 10⁹¹(92-digit number)

39711860792123617167…34154604824708465399

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

3.971 × 10⁹¹(92-digit number)

39711860792123617167…34154604824708465399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.971 × 10⁹¹(92-digit number)

39711860792123617167…34154604824708465401

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

7.942 × 10⁹¹(92-digit number)

79423721584247234334…68309209649416930799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.942 × 10⁹¹(92-digit number)

79423721584247234334…68309209649416930801

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

1.588 × 10⁹²(93-digit number)

15884744316849446866…36618419298833861599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.588 × 10⁹²(93-digit number)

15884744316849446866…36618419298833861601

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

3.176 × 10⁹²(93-digit number)

31769488633698893733…73236838597667723199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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