Block #244,037

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 3:19:40 PM · Difficulty 9.9624 · 6,554,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

920ae4cc19c5d8313da108f803c8ed34cabc241d9d4e79bf21bfd43917abfe8a

View on Chainz ↗

Height

#244,037

Difficulty

9.962421

Transactions

Size

1.94 KB

Version

Bits

09f6613e

Nonce

388

Timestamp

11/4/2013, 3:19:40 PM

Confirmations

6,554,552

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

80ceb4ea2b176b66f165bd84369326c62d1ccc3cc87d7d8af1fe6fb04933f26a

Transactions (5)

Coinbasebfc60ff816f099…d389395f0da524

1 in → 2 out10.1000 XPM136 B

AZDUEbdS…RYKMRZET AHsw4d6U…EnM8UXNZ

3d76e101dd7e1c…c4adcd02d7f63d

3 in → 2 out376.7270 XPM522 B

AYEDUQPW…DKnUBFQx AYmzdtJB…hiasyn2t

269c8bede8ad5f…bc18213c3c06ca

3 in → 2 out657.9400 XPM523 B

AK3Lao44…kfsg5ztV AMpnY1hq…bQyKMb2r

acc175a0129dbd…54dffb21b1499b

3 in → 1 out30.2300 XPM489 B

AJ6fv1Jh…AMeqVhoj

a23df0f087713c…8a6c7ad496dc1f

1 in → 2 out10.0600 XPM225 B

AdCbHMuV…xwQmtx9z ATPf4xo2…9fTHfGzg

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.

6.916 × 10⁹⁹(100-digit number)

69168188658576291162…45722399488988172799

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

6.916 × 10⁹⁹(100-digit number)

69168188658576291162…45722399488988172799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.916 × 10⁹⁹(100-digit number)

69168188658576291162…45722399488988172801

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

1.383 × 10¹⁰⁰(101-digit number)

13833637731715258232…91444798977976345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.383 × 10¹⁰⁰(101-digit number)

13833637731715258232…91444798977976345601

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

2.766 × 10¹⁰⁰(101-digit number)

27667275463430516464…82889597955952691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.766 × 10¹⁰⁰(101-digit number)

27667275463430516464…82889597955952691201

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

5.533 × 10¹⁰⁰(101-digit number)

55334550926861032929…65779195911905382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.533 × 10¹⁰⁰(101-digit number)

55334550926861032929…65779195911905382401

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

1.106 × 10¹⁰¹(102-digit number)

11066910185372206585…31558391823810764799

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