Block #443,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 4:48:02 PM · Difficulty 10.3477 · 6,366,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c909471c890579d78aa326bfada78b22a3631551be86ad29c9b922df4235db3

View on Chainz ↗

Height

#443,589

Difficulty

10.347737

Transactions

Size

1.08 KB

Version

Bits

0a59054b

Nonce

96,274

Timestamp

3/14/2014, 4:48:02 PM

Confirmations

6,366,866

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6cbaf8dc36f4941814a1eb1665a6707bde4af972037065fbace9eff75b6c3f2d

Transactions (5)

Coinbase3836cd3466011c…c1e020ebc41d0a

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

d74c4ed3c08a2d…7c0913b5f7ca09

1 in → 2 out9.2700 XPM227 B

AVtKcDbm…LK6i6QQ6 AHXsJ572…7GozNmpz

4484889a72f596…62b60fe44769c0

1 in → 2 out9.2700 XPM226 B

AXefrqBN…1MxpYJTv AcNfyX9t…hT5WFcoz

dea32542fd9cdb…6e709b35f5e37e

1 in → 2 out9.2700 XPM227 B

AJMMzTAF…UJjGF9qy ANi7XGDU…5htxGAhi

81afe1128bcb2b…0bce7a408265b5

1 in → 2 out8.2591 XPM227 B

AUyx6Zc2…aZPWCMTP AJ7tYcEj…BTHkiZ6e

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.

8.635 × 10¹⁰⁰(101-digit number)

86353406986766198744…66193872877694668799

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

8.635 × 10¹⁰⁰(101-digit number)

86353406986766198744…66193872877694668799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.635 × 10¹⁰⁰(101-digit number)

86353406986766198744…66193872877694668801

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

1.727 × 10¹⁰¹(102-digit number)

17270681397353239748…32387745755389337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.727 × 10¹⁰¹(102-digit number)

17270681397353239748…32387745755389337601

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

3.454 × 10¹⁰¹(102-digit number)

34541362794706479497…64775491510778675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.454 × 10¹⁰¹(102-digit number)

34541362794706479497…64775491510778675201

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

6.908 × 10¹⁰¹(102-digit number)

69082725589412958995…29550983021557350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.908 × 10¹⁰¹(102-digit number)

69082725589412958995…29550983021557350401

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

1.381 × 10¹⁰²(103-digit number)

13816545117882591799…59101966043114700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.381 × 10¹⁰²(103-digit number)

13816545117882591799…59101966043114700801

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 #443,589

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