Block #74,626

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 12:06:29 PM · Difficulty 8.9956 · 6,716,367 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a688583812b45df7c3eab2e305798e61041fdd1906ba841d9756a50ecf9b022

View on Chainz ↗

Height

#74,626

Difficulty

8.995626

Transactions

Size

198 B

Version

Bits

08fee159

Nonce

858

Timestamp

7/21/2013, 12:06:29 PM

Confirmations

6,716,367

Merkle Root

6b24c091255fca784afe1ffa8e63993caf8bd20cada47313bc5d66a032cd9747

Transactions (1)

Coinbase6b24c091255fca…5d66a032cd9747

1 in → 1 out12.3400 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.453 × 10⁹¹(92-digit number)

14533909996055240796…59900408441192708329

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

1.453 × 10⁹¹(92-digit number)

14533909996055240796…59900408441192708329

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.453 × 10⁹¹(92-digit number)

14533909996055240796…59900408441192708331

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

2.906 × 10⁹¹(92-digit number)

29067819992110481592…19800816882385416659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.906 × 10⁹¹(92-digit number)

29067819992110481592…19800816882385416661

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

5.813 × 10⁹¹(92-digit number)

58135639984220963185…39601633764770833319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.813 × 10⁹¹(92-digit number)

58135639984220963185…39601633764770833321

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

1.162 × 10⁹²(93-digit number)

11627127996844192637…79203267529541666639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.162 × 10⁹²(93-digit number)

11627127996844192637…79203267529541666641

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

2.325 × 10⁹²(93-digit number)

23254255993688385274…58406535059083333279

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