Block #452,585

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 4:38:29 PM · Difficulty 10.3908 · 6,350,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a23c6b9e698b6ff192d238513f86b58928ba8f8554087525a9e034382dd0407c

View on Chainz ↗

Height

#452,585

Difficulty

10.390795

Transactions

Size

834 B

Version

Bits

0a640b21

Nonce

48,495

Timestamp

3/20/2014, 4:38:29 PM

Confirmations

6,350,927

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

87a2ecb8281658d9a6e2877c11228e5801aa3f98ed3bc219e1fc9701738ed82e

Transactions (1)

Coinbase87a2ecb8281658…fc9701738ed82e

1 in → 20 out9.2500 XPM743 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH ASgUri65…C7NLcyBg AUzEPJFG…kYkA5U9V

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.

2.094 × 10⁹⁷(98-digit number)

20941309362955523117…34784966229414502439

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

2.094 × 10⁹⁷(98-digit number)

20941309362955523117…34784966229414502439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.094 × 10⁹⁷(98-digit number)

20941309362955523117…34784966229414502441

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

4.188 × 10⁹⁷(98-digit number)

41882618725911046235…69569932458829004879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.188 × 10⁹⁷(98-digit number)

41882618725911046235…69569932458829004881

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

8.376 × 10⁹⁷(98-digit number)

83765237451822092470…39139864917658009759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.376 × 10⁹⁷(98-digit number)

83765237451822092470…39139864917658009761

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

1.675 × 10⁹⁸(99-digit number)

16753047490364418494…78279729835316019519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.675 × 10⁹⁸(99-digit number)

16753047490364418494…78279729835316019521

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

3.350 × 10⁹⁸(99-digit number)

33506094980728836988…56559459670632039039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.350 × 10⁹⁸(99-digit number)

33506094980728836988…56559459670632039041

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