Block #362,571

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 7:33:23 PM · Difficulty 10.4148 · 6,446,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c4f8e321dc39b72369128041413c517167e9eb93e20d4308342b77ba8a69109

View on Chainz ↗

Height

#362,571

Difficulty

10.414834

Transactions

Size

1.95 KB

Version

Bits

0a6a3296

Nonce

58,580

Timestamp

1/16/2014, 7:33:23 PM

Confirmations

6,446,989

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2821658e6ff0e8fdece071c9fcff8b44b6989e2824c79b6fbea2605346b91c24

Transactions (5)

Coinbase22c9c8f64df6cc…5c06ab0dd6963c

1 in → 1 out9.2600 XPM110 B

AeKNrjNj…1NEq95Ta

ad6d427fa45193…365309b9a8bc4b

6 in → 2 out50.0466 XPM967 B

AbY5NcBz…yJPDKCMv AVSAFSyk…FJaJFDZ3

f53f47c5fe67c2…8266baf8488f96

2 in → 2 out11.3185 XPM374 B

Ae2k2jsQ…pXjhaKSQ AVqhrUi1…TCaf1t6i

8674425899d4f8…d9a845ca44932d

1 in → 2 out8.2273 XPM225 B

AdQy6e87…qSs8PQU7 AUihKxG5…tx8Mv8G8

8fd9f13073e065…245ccc4de15bc0

1 in → 2 out6.2016 XPM227 B

AVJ854op…WToi3kbj AWhqCNs1…mTz9bU71

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.

1.351 × 10⁹⁸(99-digit number)

13514766443634007340…62995192375620646399

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

1.351 × 10⁹⁸(99-digit number)

13514766443634007340…62995192375620646399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.351 × 10⁹⁸(99-digit number)

13514766443634007340…62995192375620646401

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

2.702 × 10⁹⁸(99-digit number)

27029532887268014681…25990384751241292799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.702 × 10⁹⁸(99-digit number)

27029532887268014681…25990384751241292801

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

5.405 × 10⁹⁸(99-digit number)

54059065774536029362…51980769502482585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.405 × 10⁹⁸(99-digit number)

54059065774536029362…51980769502482585601

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

1.081 × 10⁹⁹(100-digit number)

10811813154907205872…03961539004965171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.081 × 10⁹⁹(100-digit number)

10811813154907205872…03961539004965171201

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

2.162 × 10⁹⁹(100-digit number)

21623626309814411744…07923078009930342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.162 × 10⁹⁹(100-digit number)

21623626309814411744…07923078009930342401

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 #362,571

Cookie Preferences