Block #6,784,913

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2026, 10:39:09 PM · Difficulty 10.9809 · 6,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2bde51192261fa460df5094a02bdc62d4a6049e0efd9fd66fdbb4f2255000818

View on Chainz ↗

Height

#6,784,913

Difficulty

10.980853

Transactions

Size

191 B

Version

536870912

Bits

0afb192c

Nonce

938,621,741

Timestamp

4/5/2026, 10:39:09 PM

Confirmations

6,797

Merkle Root

8e786337633d2213d504ec647c1dab13620da5e854c9493d614ed438d56c590c

Transactions (1)

Coinbase8e786337633d22…4ed438d56c590c

1 in → 1 out8.1790 XPM101 B

AMrLYUQN…jwjifxiz

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.

2.854 × 10⁹⁴(95-digit number)

28541589003536898784…97758784821063797279

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

2.854 × 10⁹⁴(95-digit number)

28541589003536898784…97758784821063797279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.854 × 10⁹⁴(95-digit number)

28541589003536898784…97758784821063797281

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

5.708 × 10⁹⁴(95-digit number)

57083178007073797568…95517569642127594559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.708 × 10⁹⁴(95-digit number)

57083178007073797568…95517569642127594561

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

1.141 × 10⁹⁵(96-digit number)

11416635601414759513…91035139284255189119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.141 × 10⁹⁵(96-digit number)

11416635601414759513…91035139284255189121

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

2.283 × 10⁹⁵(96-digit number)

22833271202829519027…82070278568510378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.283 × 10⁹⁵(96-digit number)

22833271202829519027…82070278568510378241

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

4.566 × 10⁹⁵(96-digit number)

45666542405659038054…64140557137020756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.566 × 10⁹⁵(96-digit number)

45666542405659038054…64140557137020756481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.133 × 10⁹⁵(96-digit number)

91333084811318076109…28281114274041512959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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