Block #446,641

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 3/16/2014, 5:20:16 PM · Difficulty 10.3597 · 6,363,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43430e5ef30db0da3f0acf415f80fa22678df54a4b693117f8840e16a635b234

View on Chainz ↗

Height

#446,641

Difficulty

10.359676

Transactions

Size

24.94 KB

Version

Bits

0a5c13be

Nonce

7,067

Timestamp

3/16/2014, 5:20:16 PM

Confirmations

6,363,035

Mined by

⛏️ aS%AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0901ca75fc723683bb0d183d5224c30f9004b2b5b82b3a2d795bc0739cb04739

Transactions (2)

Coinbase01f91ccff245af…8e9c228631b107

1 in → 26 out9.3000 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

06c0d1679e6bfc…c54850abc280f3

165 in → 2 out1378.0101 XPM23.92 KB

AbQJ6nQg…5yP8qjjW ASHbrZpC…MLpBSios

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.

1.742 × 10⁹⁸(99-digit number)

17426462218941498704…05763465251524991999

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

1.742 × 10⁹⁸(99-digit number)

17426462218941498704…05763465251524991999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.742 × 10⁹⁸(99-digit number)

17426462218941498704…05763465251524992001

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

3.485 × 10⁹⁸(99-digit number)

34852924437882997408…11526930503049983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.485 × 10⁹⁸(99-digit number)

34852924437882997408…11526930503049984001

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

6.970 × 10⁹⁸(99-digit number)

69705848875765994817…23053861006099967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.970 × 10⁹⁸(99-digit number)

69705848875765994817…23053861006099968001

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

1.394 × 10⁹⁹(100-digit number)

13941169775153198963…46107722012199935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.394 × 10⁹⁹(100-digit number)

13941169775153198963…46107722012199936001

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

2.788 × 10⁹⁹(100-digit number)

27882339550306397927…92215444024399871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.788 × 10⁹⁹(100-digit number)

27882339550306397927…92215444024399872001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.576 × 10⁹⁹(100-digit number)

55764679100612795854…84430888048799743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

5.576 × 10⁹⁹(100-digit number)

55764679100612795854…84430888048799744001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #446,641

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