Block #382,854

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 12:57:29 AM · Difficulty 10.3977 · 6,444,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

deef97e6260083ada293c4542480ce647e92d2bd46c3e389307e9ae7861143bf

View on Chainz ↗

Height

#382,854

Difficulty

10.397673

Transactions

Size

9.22 KB

Version

Bits

0a65cde3

Nonce

4,002

Timestamp

1/31/2014, 12:57:29 AM

Confirmations

6,444,150

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0774d91c7fd0950c8f9830a03faf1807b968d32861b63a34895f4ad7b79ad497

Transactions (4)

Coinbase439dc583d82d36…e62d12ebae3cc6

1 in → 1 out9.3585 XPM116 B

AbwWkWZt…kawDhufa

a03499c9046d43…f4645959a556a7

3 in → 2 out235.6488 XPM524 B

AHh6SpmU…BS9dmDLJ AHPuhHnK…xEdBN2JY

31744a34af9293…7b8a65837f5a79

1 in → 2 out9.1900 XPM225 B

AeeYKx3v…1UV5JMFi AK5vqVts…4FhCHKz7

90d7b04940a59a…317e1b09d31641

57 in → 1 out18.2100 XPM8.28 KB

AXUDMymf…T7c5qBsq

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.

9.171 × 10¹⁰³(104-digit number)

91719969872095014019…22861444768399040649

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

9.171 × 10¹⁰³(104-digit number)

91719969872095014019…22861444768399040649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.171 × 10¹⁰³(104-digit number)

91719969872095014019…22861444768399040651

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

1.834 × 10¹⁰⁴(105-digit number)

18343993974419002803…45722889536798081299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.834 × 10¹⁰⁴(105-digit number)

18343993974419002803…45722889536798081301

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

3.668 × 10¹⁰⁴(105-digit number)

36687987948838005607…91445779073596162599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.668 × 10¹⁰⁴(105-digit number)

36687987948838005607…91445779073596162601

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

7.337 × 10¹⁰⁴(105-digit number)

73375975897676011215…82891558147192325199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.337 × 10¹⁰⁴(105-digit number)

73375975897676011215…82891558147192325201

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

1.467 × 10¹⁰⁵(106-digit number)

14675195179535202243…65783116294384650399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.467 × 10¹⁰⁵(106-digit number)

14675195179535202243…65783116294384650401

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 #382,854

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