Block #427,453

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 9:23:31 AM · Difficulty 10.3492 · 6,379,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

970c6f736431a528f890f19b052052e46fa48b1b8c858d4518b435607dce4821

View on Chainz ↗

Height

#427,453

Difficulty

10.349216

Transactions

Size

800 B

Version

Bits

0a596631

Nonce

446,502

Timestamp

3/3/2014, 9:23:31 AM

Confirmations

6,379,686

Mined by

⛏️ iAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

556e8ace3d969540ae4d5d898b4cbe173ed5c535d20fa83c5d3bcff7bfca01cd

Transactions (1)

Coinbase556e8ace3d9695…3bcff7bfca01cd

1 in → 19 out9.3200 XPM709 B

AdFLJFhb…bsaVkAyh AZqjMFvv…G8aw2zC8 AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx AQFhQpUS…HmKbSyAx

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.

1.971 × 10⁹⁸(99-digit number)

19710135180614651691…19952181671996795199

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

1.971 × 10⁹⁸(99-digit number)

19710135180614651691…19952181671996795199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.971 × 10⁹⁸(99-digit number)

19710135180614651691…19952181671996795201

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

3.942 × 10⁹⁸(99-digit number)

39420270361229303383…39904363343993590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.942 × 10⁹⁸(99-digit number)

39420270361229303383…39904363343993590401

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

7.884 × 10⁹⁸(99-digit number)

78840540722458606767…79808726687987180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.884 × 10⁹⁸(99-digit number)

78840540722458606767…79808726687987180801

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

1.576 × 10⁹⁹(100-digit number)

15768108144491721353…59617453375974361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.576 × 10⁹⁹(100-digit number)

15768108144491721353…59617453375974361601

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

3.153 × 10⁹⁹(100-digit number)

31536216288983442707…19234906751948723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.153 × 10⁹⁹(100-digit number)

31536216288983442707…19234906751948723201

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 #427,453

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