Block #249,066

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 5:59:38 PM · Difficulty 9.9665 · 6,565,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0ad7a9cb157a6747eaad74c277dc1a2f2e8ac3622e85247b1182dc010c6d576

View on Chainz ↗

Height

#249,066

Difficulty

9.966493

Transactions

Size

1.82 KB

Version

Bits

09f76c15

Nonce

5,736

Timestamp

11/7/2013, 5:59:38 PM

Confirmations

6,565,983

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

c0c6471711877b6e8554d3ae071eda3c891cbe32db4740f9f429bdb92b5dc6b2

Transactions (3)

Coinbase501260dacb0a22…f9dd128b645e5b

1 in → 2 out10.0800 XPM137 B

AZDUEbdS…RYKMRZET AU6kq4CL…dQBLvxLp

363fcf3fc5e471…e1f83b3d888366

2 in → 2 out20.1100 XPM375 B

ALsqSwWV…uZ7sTz8x AepziSiP…uLB2L8Mm

83a3507da50779…7acb8351e45ad5

8 in → 2 out50.0510 XPM1.23 KB

ATP59UD7…DAp7CaGB AQ2jX9CT…mEUPvyzY

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.

1.146 × 10⁹⁷(98-digit number)

11462971194966740329…81315189485331548159

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

1.146 × 10⁹⁷(98-digit number)

11462971194966740329…81315189485331548159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.146 × 10⁹⁷(98-digit number)

11462971194966740329…81315189485331548161

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

2.292 × 10⁹⁷(98-digit number)

22925942389933480658…62630378970663096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.292 × 10⁹⁷(98-digit number)

22925942389933480658…62630378970663096321

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

4.585 × 10⁹⁷(98-digit number)

45851884779866961316…25260757941326192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.585 × 10⁹⁷(98-digit number)

45851884779866961316…25260757941326192641

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

9.170 × 10⁹⁷(98-digit number)

91703769559733922633…50521515882652385279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.170 × 10⁹⁷(98-digit number)

91703769559733922633…50521515882652385281

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

1.834 × 10⁹⁸(99-digit number)

18340753911946784526…01043031765304770559

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

Block #249,066

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