Block #454,176

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 6:36:48 PM · Difficulty 10.3955 · 6,356,538 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

506601a1fc1ea462f7ace5c0e0454b5ea66d019e407b26b1f77a951f1cf3f1a2

View on Chainz ↗

Height

#454,176

Difficulty

10.395512

Transactions

Size

903 B

Version

Bits

0a654043

Nonce

29,955

Timestamp

3/21/2014, 6:36:48 PM

Confirmations

6,356,538

Mined by

⛏️ kAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

afe220fab66c95824f6ea5f00ee59d90e87e31dff8972a353587e0c70e54e10a

Transactions (1)

Coinbaseafe220fab66c95…87e0c70e54e10a

1 in → 22 out9.2400 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg ATp4jJhs…TbSgR8Qb AWFABhGb…QWK99PRN

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.

9.754 × 10⁹⁹(100-digit number)

97548665590931375653…47881081369419479039

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

9.754 × 10⁹⁹(100-digit number)

97548665590931375653…47881081369419479039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.754 × 10⁹⁹(100-digit number)

97548665590931375653…47881081369419479041

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

1.950 × 10¹⁰⁰(101-digit number)

19509733118186275130…95762162738838958079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.950 × 10¹⁰⁰(101-digit number)

19509733118186275130…95762162738838958081

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

3.901 × 10¹⁰⁰(101-digit number)

39019466236372550261…91524325477677916159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.901 × 10¹⁰⁰(101-digit number)

39019466236372550261…91524325477677916161

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

7.803 × 10¹⁰⁰(101-digit number)

78038932472745100522…83048650955355832319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.803 × 10¹⁰⁰(101-digit number)

78038932472745100522…83048650955355832321

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

1.560 × 10¹⁰¹(102-digit number)

15607786494549020104…66097301910711664639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.560 × 10¹⁰¹(102-digit number)

15607786494549020104…66097301910711664641

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 #454,176

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