Block #440,897

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 5:59:32 PM · Difficulty 10.3534 · 6,362,762 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

baefad94b3a5684016d313bd94929b9b07844a2b9df69ffcd823c054390e8dd5

View on Chainz ↗

Height

#440,897

Difficulty

10.353441

Transactions

Size

1.01 KB

Version

Bits

0a5a7b1e

Nonce

74,291

Timestamp

3/12/2014, 5:59:32 PM

Confirmations

6,362,762

Mined by

⛏️ AaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

328cb97c0687862dc903fe9fc8eb1b61ff58fb1744b295ad846d5fd2d9fb0e00

Transactions (1)

Coinbase328cb97c068786…6d5fd2d9fb0e00

1 in → 26 out9.3100 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR AScAzqGc…BZ6tV1vJ

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.

1.402 × 10⁹⁹(100-digit number)

14025269050153989140…67627084001689595999

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

1.402 × 10⁹⁹(100-digit number)

14025269050153989140…67627084001689595999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.402 × 10⁹⁹(100-digit number)

14025269050153989140…67627084001689596001

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

2.805 × 10⁹⁹(100-digit number)

28050538100307978281…35254168003379191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.805 × 10⁹⁹(100-digit number)

28050538100307978281…35254168003379192001

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

5.610 × 10⁹⁹(100-digit number)

56101076200615956563…70508336006758383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.610 × 10⁹⁹(100-digit number)

56101076200615956563…70508336006758384001

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

1.122 × 10¹⁰⁰(101-digit number)

11220215240123191312…41016672013516767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.122 × 10¹⁰⁰(101-digit number)

11220215240123191312…41016672013516768001

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

2.244 × 10¹⁰⁰(101-digit number)

22440430480246382625…82033344027033535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.244 × 10¹⁰⁰(101-digit number)

22440430480246382625…82033344027033536001

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