Block #2,641,125

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 6:05:31 AM · Difficulty 11.6081 · 4,196,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56f89cfcaf4a29a5a764362335058f007467bc9c5c395de2b839c2d93f2cbe0b

View on Chainz ↗

Height

#2,641,125

Difficulty

11.608079

Transactions

Size

425 B

Version

Bits

0b9bab17

Nonce

461,291,283

Timestamp

5/1/2018, 6:05:31 AM

Confirmations

4,196,977

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e05174332a420eda63dc896aa4d0865e66370351624b198a9cb6780f72bb6135

Transactions (2)

Coinbased1a18fe95f1ea7…d79a983fd96854

1 in → 1 out7.4200 XPM109 B

Adqah8zh…1WwoHJ9t

b4445dcb8a2994…4db65bc3ae9eb6

1 in → 2 out3.9900 XPM226 B

AQtMZxfv…SFiMbpLQ AKCSvoxS…pqXFEBhu

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.

3.799 × 10⁹⁵(96-digit number)

37994398138533172809…42302707636238131199

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

3.799 × 10⁹⁵(96-digit number)

37994398138533172809…42302707636238131199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.799 × 10⁹⁵(96-digit number)

37994398138533172809…42302707636238131201

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

7.598 × 10⁹⁵(96-digit number)

75988796277066345618…84605415272476262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.598 × 10⁹⁵(96-digit number)

75988796277066345618…84605415272476262401

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

1.519 × 10⁹⁶(97-digit number)

15197759255413269123…69210830544952524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.519 × 10⁹⁶(97-digit number)

15197759255413269123…69210830544952524801

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

3.039 × 10⁹⁶(97-digit number)

30395518510826538247…38421661089905049599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.039 × 10⁹⁶(97-digit number)

30395518510826538247…38421661089905049601

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

6.079 × 10⁹⁶(97-digit number)

60791037021653076494…76843322179810099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.079 × 10⁹⁶(97-digit number)

60791037021653076494…76843322179810099201

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

1.215 × 10⁹⁷(98-digit number)

12158207404330615298…53686644359620198399

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

Block #2,641,125

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