Block #443,647

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 4:56:38 PM · Difficulty 10.3466 · 6,383,004 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd9f3639146786129d27ea11cfc3e97c28b745ca469ad4c5e2298a9780cc1f1c

View on Chainz ↗

Height

#443,647

Difficulty

10.346617

Transactions

Size

2.18 KB

Version

Bits

0a58bbdf

Nonce

109,857

Timestamp

3/14/2014, 4:56:38 PM

Confirmations

6,383,004

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

2fc04470d22ab9c5194a940ddf2ad91a5580e915f15dc5ba99187928b0908129

Transactions (4)

Coinbaseb0e2a677dfa7d9…af24840452c9a8

1 in → 21 out9.3600 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AMW1p9oT…2TzdaZxH ASgUri65…C7NLcyBg

198a33f3f35cd3…7c99667e099a15

4 in → 13 out37.2700 XPM910 B

AMWKZVBD…MdPAD8q6 AHDXF3Ls…Vg5V84qr Aez1R54Z…Z4JrdVbN AVXqAjBB…2RxF5Hqg AeKNrjNj…1NEq95Ta

84c15903702d6b…a79170869c7334

1 in → 2 out3.2041 XPM226 B

ASfQj9Pb…Q87HBF2g AUZd8nge…r8K4RZeX

eac29823f1dde3…aa233883d6e6d7

1 in → 2 out3.2270 XPM227 B

AR5fhzo6…W2MW35Y6 AXiqk2Lr…qt278fqb

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.

1.259 × 10⁹⁴(95-digit number)

12591712994515966259…45456305658657046399

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

1.259 × 10⁹⁴(95-digit number)

12591712994515966259…45456305658657046399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.259 × 10⁹⁴(95-digit number)

12591712994515966259…45456305658657046401

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

2.518 × 10⁹⁴(95-digit number)

25183425989031932518…90912611317314092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.518 × 10⁹⁴(95-digit number)

25183425989031932518…90912611317314092801

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

5.036 × 10⁹⁴(95-digit number)

50366851978063865036…81825222634628185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.036 × 10⁹⁴(95-digit number)

50366851978063865036…81825222634628185601

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

1.007 × 10⁹⁵(96-digit number)

10073370395612773007…63650445269256371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.007 × 10⁹⁵(96-digit number)

10073370395612773007…63650445269256371201

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

2.014 × 10⁹⁵(96-digit number)

20146740791225546014…27300890538512742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.014 × 10⁹⁵(96-digit number)

20146740791225546014…27300890538512742401

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 #443,647

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