Block #432,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 9:24:05 PM · Difficulty 10.3423 · 6,371,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6420f10cde62c67871cc1b32379abb70bf4aa2daeead6c3d99274abaa264609c

View on Chainz ↗

Height

#432,414

Difficulty

10.342310

Transactions

Size

1.01 KB

Version

Bits

0a57a199

Nonce

4,177

Timestamp

3/6/2014, 9:24:05 PM

Confirmations

6,371,266

Mined by

⛏️ aS%AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c22ad69b9720d0839d56986925da72f204f820460705f22168ab59bf49676c87

Transactions (1)

Coinbasec22ad69b9720d0…ab59bf49676c87

1 in → 26 out9.3300 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

2.787 × 10⁹⁵(96-digit number)

27871656316699140350…17137208818124249599

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

2.787 × 10⁹⁵(96-digit number)

27871656316699140350…17137208818124249599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.787 × 10⁹⁵(96-digit number)

27871656316699140350…17137208818124249601

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

5.574 × 10⁹⁵(96-digit number)

55743312633398280700…34274417636248499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.574 × 10⁹⁵(96-digit number)

55743312633398280700…34274417636248499201

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

1.114 × 10⁹⁶(97-digit number)

11148662526679656140…68548835272496998399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.114 × 10⁹⁶(97-digit number)

11148662526679656140…68548835272496998401

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

2.229 × 10⁹⁶(97-digit number)

22297325053359312280…37097670544993996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.229 × 10⁹⁶(97-digit number)

22297325053359312280…37097670544993996801

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

4.459 × 10⁹⁶(97-digit number)

44594650106718624560…74195341089987993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.459 × 10⁹⁶(97-digit number)

44594650106718624560…74195341089987993601

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