Block #456,171

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 1:07:45 AM · Difficulty 10.4167 · 6,333,901 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c26ece5822e330ed827c8ae123e0de3e931a5b99c874c4624764ea66a8d416b

View on Chainz ↗

Height

#456,171

Difficulty

10.416749

Transactions

Size

5.55 KB

Version

Bits

0a6ab015

Nonce

890,684

Timestamp

3/23/2014, 1:07:45 AM

Confirmations

6,333,901

Merkle Root

046ed5214a97fb74de3e614068ea0516e742550c065d293e85ad268c96e5ee79

Transactions (3)

Coinbasec4464ec89280fb…88efd35919f57e

1 in → 1 out9.2700 XPM109 B

AUsgTN6t…qJNEX1dq

a3df40445f413c…75832317911486

19 in → 2 out19.0076 XPM2.82 KB

AQCtKXJ7…5wWGk6Zk AaaWv4yp…XD6fSm7L

b4971842b903c8…2ab1ac9bcaf405

17 in → 2 out15.1027 XPM2.53 KB

AaaWv4yp…XD6fSm7L ATKfBm8B…qJcXQ71R

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.

1.093 × 10⁹⁵(96-digit number)

10935050638986265864…99436481715311701199

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

1.093 × 10⁹⁵(96-digit number)

10935050638986265864…99436481715311701199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.093 × 10⁹⁵(96-digit number)

10935050638986265864…99436481715311701201

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

2.187 × 10⁹⁵(96-digit number)

21870101277972531729…98872963430623402399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.187 × 10⁹⁵(96-digit number)

21870101277972531729…98872963430623402401

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

4.374 × 10⁹⁵(96-digit number)

43740202555945063458…97745926861246804799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.374 × 10⁹⁵(96-digit number)

43740202555945063458…97745926861246804801

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

8.748 × 10⁹⁵(96-digit number)

87480405111890126917…95491853722493609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.748 × 10⁹⁵(96-digit number)

87480405111890126917…95491853722493609601

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

1.749 × 10⁹⁶(97-digit number)

17496081022378025383…90983707444987219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.749 × 10⁹⁶(97-digit number)

17496081022378025383…90983707444987219201

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