Block #425,835

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 5:08:51 AM · Difficulty 10.3581 · 6,377,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de29c1ab1db86416cb58514d8ff172fb1fd052cccc0968643cbc310f816eeb41

View on Chainz ↗

Height

#425,835

Difficulty

10.358118

Transactions

Size

937 B

Version

Bits

0a5bada4

Nonce

6,566

Timestamp

3/2/2014, 5:08:51 AM

Confirmations

6,377,443

Mined by

⛏️ kaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

260a25cb386767b97036ebcb07845599eb2a443096519090b25032e02ed93284

Transactions (1)

Coinbase260a25cb386767…5032e02ed93284

1 in → 23 out9.3100 XPM845 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

1.673 × 10¹⁰⁰(101-digit number)

16739389378103847321…24198313662332441599

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

1.673 × 10¹⁰⁰(101-digit number)

16739389378103847321…24198313662332441599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.673 × 10¹⁰⁰(101-digit number)

16739389378103847321…24198313662332441601

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

3.347 × 10¹⁰⁰(101-digit number)

33478778756207694643…48396627324664883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.347 × 10¹⁰⁰(101-digit number)

33478778756207694643…48396627324664883201

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

6.695 × 10¹⁰⁰(101-digit number)

66957557512415389287…96793254649329766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.695 × 10¹⁰⁰(101-digit number)

66957557512415389287…96793254649329766401

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

1.339 × 10¹⁰¹(102-digit number)

13391511502483077857…93586509298659532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.339 × 10¹⁰¹(102-digit number)

13391511502483077857…93586509298659532801

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

2.678 × 10¹⁰¹(102-digit number)

26783023004966155715…87173018597319065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.678 × 10¹⁰¹(102-digit number)

26783023004966155715…87173018597319065601

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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