Block #382,323

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 3:02:47 PM · Difficulty 10.4050 · 6,411,871 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0bdc855ad2d77e9066e58b139325b869ef73c368e082ff531131bee72fc19e9

View on Chainz ↗

Height

#382,323

Difficulty

10.405023

Transactions

Size

1.80 KB

Version

Bits

0a67af95

Nonce

50,206

Timestamp

1/30/2014, 3:02:47 PM

Confirmations

6,411,871

Merkle Root

4013bfa697ee9c4ee1b74c7089da024f4d4c9f67765e7af34b10499587961f01

Transactions (5)

Coinbase06984b106eda95…88395f068177f0

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

f61c5166860b30…653147dead5153

1 in → 2 out7.1009 XPM226 B

AR6aSJNi…qcxiqeVf ASaAmLQB…95eBPcq2

7ec147fbea56c1…69f01f7561adb6

1 in → 2 out4.0882 XPM225 B

AGsqyceB…BN5iMQE4 AK6pzD6g…BJbkP6wD

8b68bd5d23681d…d585e94f65f509

1 in → 2 out3.3867 XPM226 B

AVGgeHqG…st6CrWsp AdKHDNNN…oLRN3jaM

a962b9cba8fc3c…e9d078b804b8d4

6 in → 2 out2.0141 XPM964 B

Acysrk7N…Aemcn21x AaR8qCns…H6zPViHm

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.

9.657 × 10⁹⁴(95-digit number)

96573635762741427193…28273127187213683359

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

9.657 × 10⁹⁴(95-digit number)

96573635762741427193…28273127187213683359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.657 × 10⁹⁴(95-digit number)

96573635762741427193…28273127187213683361

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

1.931 × 10⁹⁵(96-digit number)

19314727152548285438…56546254374427366719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.931 × 10⁹⁵(96-digit number)

19314727152548285438…56546254374427366721

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

3.862 × 10⁹⁵(96-digit number)

38629454305096570877…13092508748854733439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.862 × 10⁹⁵(96-digit number)

38629454305096570877…13092508748854733441

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

7.725 × 10⁹⁵(96-digit number)

77258908610193141754…26185017497709466879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.725 × 10⁹⁵(96-digit number)

77258908610193141754…26185017497709466881

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

1.545 × 10⁹⁶(97-digit number)

15451781722038628350…52370034995418933759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.545 × 10⁹⁶(97-digit number)

15451781722038628350…52370034995418933761

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