Block #434,557

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2014, 8:29:56 AM · Difficulty 10.3482 · 6,380,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cdb8d087d608101af29799a7e8b09d4cf00c46ff00e21cffd382cab877e1937b

View on Chainz ↗

Height

#434,557

Difficulty

10.348204

Transactions

Size

3.05 KB

Version

Bits

0a5923ec

Nonce

433,832

Timestamp

3/8/2014, 8:29:56 AM

Confirmations

6,380,434

Mined by

⛏️ }YAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a9637e14383512755f09c5ed83de8910a194a5006ec6c5bf2fe0b34d907b3233

Transactions (2)

Coinbase4b7cde9cba8e78…b5f4d6cf4f2f97

1 in → 24 out9.3500 XPM879 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AVRMvm7T…6PC6keBx AZqjMFvv…G8aw2zC8 AcuM7XiJ…5uND8Jce

395fe7f46e7483…f3ecd8de371074

14 in → 2 out50.0503 XPM2.10 KB

AQHgSYkg…TxKTbeRq APqNRHhh…wKNy9QKf

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.

6.264 × 10⁹⁷(98-digit number)

62647660227870596167…08339718514247393279

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

6.264 × 10⁹⁷(98-digit number)

62647660227870596167…08339718514247393279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.264 × 10⁹⁷(98-digit number)

62647660227870596167…08339718514247393281

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

1.252 × 10⁹⁸(99-digit number)

12529532045574119233…16679437028494786559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.252 × 10⁹⁸(99-digit number)

12529532045574119233…16679437028494786561

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

2.505 × 10⁹⁸(99-digit number)

25059064091148238466…33358874056989573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.505 × 10⁹⁸(99-digit number)

25059064091148238466…33358874056989573121

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

5.011 × 10⁹⁸(99-digit number)

50118128182296476933…66717748113979146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.011 × 10⁹⁸(99-digit number)

50118128182296476933…66717748113979146241

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

1.002 × 10⁹⁹(100-digit number)

10023625636459295386…33435496227958292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.002 × 10⁹⁹(100-digit number)

10023625636459295386…33435496227958292481

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 #434,557

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