Block #140,726

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/29/2013, 8:26:23 PM · Difficulty 9.8339 · 6,686,545 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00192befc5e3035a23e10f9bb532e03829f7d3a4d988376be46f67dc15d29290

View on Chainz ↗

Height

#140,726

Difficulty

9.833895

Transactions

Size

1.64 KB

Version

Bits

09d57a23

Nonce

46,926

Timestamp

8/29/2013, 8:26:23 PM

Confirmations

6,686,545

Mined by

⛏️ P2SHATNfqMF1DH5jjvUR7kQQxc85gmTnBK5tri

Merkle Root

34e46dfd923ff74ccb2620f89b0d3daa85185a152c3f1f29bf4effdf76c888de

Transactions (2)

Coinbase7ca2a127d44f64…3968e39dc4873e

1 in → 1 out10.3500 XPM109 B

ATNfqMF1…TnBK5tri

c2dc27ca68beeb…1fc352849fb994

12 in → 2 out121.0800 XPM1.44 KB

Ad3ear2o…Je6ymxq3 AGZvBxxa…shhkwtTn

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.

4.718 × 10⁹⁰(91-digit number)

47180716332259779161…62531463024584887659

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

4.718 × 10⁹⁰(91-digit number)

47180716332259779161…62531463024584887659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.718 × 10⁹⁰(91-digit number)

47180716332259779161…62531463024584887661

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

9.436 × 10⁹⁰(91-digit number)

94361432664519558322…25062926049169775319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.436 × 10⁹⁰(91-digit number)

94361432664519558322…25062926049169775321

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

1.887 × 10⁹¹(92-digit number)

18872286532903911664…50125852098339550639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.887 × 10⁹¹(92-digit number)

18872286532903911664…50125852098339550641

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

3.774 × 10⁹¹(92-digit number)

37744573065807823329…00251704196679101279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.774 × 10⁹¹(92-digit number)

37744573065807823329…00251704196679101281

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

7.548 × 10⁹¹(92-digit number)

75489146131615646658…00503408393358202559

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 #140,726

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