Block #443,967

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 10:37:50 PM · Difficulty 10.3455 · 6,362,293 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abb6aa61f0e4d29cdbd43087e2e2fe627add53a202624fffb42c86336a37c355

View on Chainz ↗

Height

#443,967

Difficulty

10.345459

Transactions

Size

1.05 KB

Version

Bits

0a586ff8

Nonce

20,808

Timestamp

3/14/2014, 10:37:50 PM

Confirmations

6,362,293

Mined by

⛏️ P2SHAS9bktoszkM8NWvso6ikCwNdjsDWzBZ5EC

Merkle Root

872ec0830f223a840ad795df218bb533586d21433253d6a3af710946d05c8f4b

Transactions (2)

Coinbase2bfe22545f9c23…f913a00e50a6af

1 in → 1 out9.3400 XPM112 B

AS9bktos…DWzBZ5EC

6999bfa9ea6699…9e05754088226b

4 in → 12 out37.3600 XPM873 B

ALfLUkWx…6cCmwzB9 ANduR3jU…CEMsRF97 AYKiwoLg…2bSJSJ59 AUi2icYo…5k64iTPM ARY4njt1…nHyFyfP6

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.

1.421 × 10⁹⁹(100-digit number)

14219419493794180509…96073948519276586879

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

1.421 × 10⁹⁹(100-digit number)

14219419493794180509…96073948519276586879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.421 × 10⁹⁹(100-digit number)

14219419493794180509…96073948519276586881

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

2.843 × 10⁹⁹(100-digit number)

28438838987588361018…92147897038553173759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.843 × 10⁹⁹(100-digit number)

28438838987588361018…92147897038553173761

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

5.687 × 10⁹⁹(100-digit number)

56877677975176722037…84295794077106347519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.687 × 10⁹⁹(100-digit number)

56877677975176722037…84295794077106347521

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

1.137 × 10¹⁰⁰(101-digit number)

11375535595035344407…68591588154212695039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.137 × 10¹⁰⁰(101-digit number)

11375535595035344407…68591588154212695041

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

2.275 × 10¹⁰⁰(101-digit number)

22751071190070688815…37183176308425390079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.275 × 10¹⁰⁰(101-digit number)

22751071190070688815…37183176308425390081

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

Block #443,967

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