Block #457,552

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/23/2014, 11:45:29 PM · Difficulty 10.4201 · 6,345,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84d9aa7c07414cc59e762c9382d67a2375553a606dddce9d4ceeb39e2da81683

View on Chainz ↗

Height

#457,552

Difficulty

10.420128

Transactions

Size

3.01 KB

Version

Bits

0a6b8d7b

Nonce

194,091

Timestamp

3/23/2014, 11:45:29 PM

Confirmations

6,345,236

Mined by

⛏️ PAN9emqpK7dgr5Ubo53Xd9AuJhzWEnrfX7s

Merkle Root

e8e8eb524a719baaf63f7457e017658818d935a6b1be29d84c202383a8636c8a

Transactions (3)

Coinbase04410c63afe08e…e9bddc7337ad45

1 in → 5 out9.2400 XPM233 B

AN9emqpK…WEnrfX7s AHQyfiZn…sQbeqE98 AWCjgrw2…MnFAU7HX ARJu9Qoh…JpP9irBQ AZzi9Hj6…PuNWYX6G

fe6a2cd242fb27…f792d43f00f88f

9 in → 35 out82.0889 XPM2.47 KB

AZv29ja6…trEEibF5 AUkdqaxr…4jcbMUQ7 AJjhokhu…9Cjwps9g AQsqCMcB…YxgrjJnb ASqqpxAv…dTvgfRnF

8544c8930617db…e4efc814fe9f5b

1 in → 2 out1.5910 XPM225 B

APD91tri…91cUkRAY AUtg7hGQ…XFGCgqY7

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.

5.784 × 10⁹³(94-digit number)

57841213612262598675…38256832771926278999

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

5.784 × 10⁹³(94-digit number)

57841213612262598675…38256832771926278999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.784 × 10⁹³(94-digit number)

57841213612262598675…38256832771926279001

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

1.156 × 10⁹⁴(95-digit number)

11568242722452519735…76513665543852557999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.156 × 10⁹⁴(95-digit number)

11568242722452519735…76513665543852558001

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

2.313 × 10⁹⁴(95-digit number)

23136485444905039470…53027331087705115999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.313 × 10⁹⁴(95-digit number)

23136485444905039470…53027331087705116001

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

4.627 × 10⁹⁴(95-digit number)

46272970889810078940…06054662175410231999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.627 × 10⁹⁴(95-digit number)

46272970889810078940…06054662175410232001

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

9.254 × 10⁹⁴(95-digit number)

92545941779620157881…12109324350820463999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.254 × 10⁹⁴(95-digit number)

92545941779620157881…12109324350820464001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.850 × 10⁹⁵(96-digit number)

18509188355924031576…24218648701640927999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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