Block #438,794

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 6:25:52 AM · Difficulty 10.3558 · 6,357,724 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bc4b3ea6db2e8055ec3be1545ba6aedeed1006f32c270db536a2a690db1dfa1

View on Chainz ↗

Height

#438,794

Difficulty

10.355841

Transactions

Size

1.38 KB

Version

Bits

0a5b1862

Nonce

13,692

Timestamp

3/11/2014, 6:25:52 AM

Confirmations

6,357,724

Mined by

⛏️ aSg*AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

61b7056d9c09432c6fceac1734246bebb2a5578599e8b85446b0cd3d60bbe2d9

Transactions (2)

Coinbasea3000085ce651b…5284f0a9d512ac

1 in → 23 out9.3025 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

b45d3357b58c98…f7227a0bc06695

2 in → 7 out18.6300 XPM477 B

AdS35fz7…hZcPixQV AJaQENaD…wRN4nbo6 AeKNrjNj…1NEq95Ta AYXvVfjC…pKH3vp2n AJ1Rg4tk…5YkqEmTH

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.

1.597 × 10⁹⁹(100-digit number)

15978676642592009330…02591498956485370879

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

1.597 × 10⁹⁹(100-digit number)

15978676642592009330…02591498956485370879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.597 × 10⁹⁹(100-digit number)

15978676642592009330…02591498956485370881

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

3.195 × 10⁹⁹(100-digit number)

31957353285184018661…05182997912970741759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.195 × 10⁹⁹(100-digit number)

31957353285184018661…05182997912970741761

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

6.391 × 10⁹⁹(100-digit number)

63914706570368037323…10365995825941483519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.391 × 10⁹⁹(100-digit number)

63914706570368037323…10365995825941483521

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

1.278 × 10¹⁰⁰(101-digit number)

12782941314073607464…20731991651882967039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.278 × 10¹⁰⁰(101-digit number)

12782941314073607464…20731991651882967041

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

2.556 × 10¹⁰⁰(101-digit number)

25565882628147214929…41463983303765934079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.556 × 10¹⁰⁰(101-digit number)

25565882628147214929…41463983303765934081

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