Block #432,421

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 9:29:14 PM · Difficulty 10.3425 · 6,360,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ac5bbcbcdad9a732c95ff6cc186eb0bcf789f88d5b8c08385a22d37451a3133

View on Chainz ↗

Height

#432,421

Difficulty

10.342508

Transactions

Size

2.39 KB

Version

Bits

0a57ae98

Nonce

12,259

Timestamp

3/6/2014, 9:29:14 PM

Confirmations

6,360,226

Merkle Root

5e35c71bdb384776ff2598b25244ce4587afc8120519221b9c5bd40bb3e1154b

Transactions (4)

Coinbased8c566dbffad92…726ceb5be88176

1 in → 23 out9.3300 XPM845 B

AQvZBsUo…hppgRZTJ Aaffr4EL…bJQCxKCY Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

488217d21ce4e0…3b58dfc6d436ab

5 in → 13 out38.6926 XPM1.03 KB

AWZcpbCB…2t2PoGkJ AdSXFDPP…ANJyvdi7 Aai7rmvE…JWhtS5Q5 AazfaUAJ…WaQjuUwm AYH3TsEE…z8QwfCk6

ccad8859ad8472…552155a5cd9a06

1 in → 2 out7.1847 XPM226 B

ATjwywoV…ga9eRXwi AHvz3a3W…QvXgJvd7

00f8b9a749a474…e688fe386904fa

1 in → 2 out4.1487 XPM226 B

AGHQBt42…kioRggo7 Aa4z7ZUc…pWg7MBRb

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.

8.721 × 10¹⁰⁰(101-digit number)

87217287046838368319…71839692864508721359

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

8.721 × 10¹⁰⁰(101-digit number)

87217287046838368319…71839692864508721359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.721 × 10¹⁰⁰(101-digit number)

87217287046838368319…71839692864508721361

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

1.744 × 10¹⁰¹(102-digit number)

17443457409367673663…43679385729017442719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.744 × 10¹⁰¹(102-digit number)

17443457409367673663…43679385729017442721

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

3.488 × 10¹⁰¹(102-digit number)

34886914818735347327…87358771458034885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.488 × 10¹⁰¹(102-digit number)

34886914818735347327…87358771458034885441

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

6.977 × 10¹⁰¹(102-digit number)

69773829637470694655…74717542916069770879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.977 × 10¹⁰¹(102-digit number)

69773829637470694655…74717542916069770881

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

1.395 × 10¹⁰²(103-digit number)

13954765927494138931…49435085832139541759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.395 × 10¹⁰²(103-digit number)

13954765927494138931…49435085832139541761

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