Block #365,341

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 4:30:34 PM · Difficulty 10.4247 · 6,450,921 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07fd8831e8c606b2ee69c36f398304001a344e14b5f7a943254011f1214a295c

View on Chainz ↗

Height

#365,341

Difficulty

10.424707

Transactions

Size

1.27 KB

Version

Bits

0a6cb998

Nonce

181,147

Timestamp

1/18/2014, 4:30:34 PM

Confirmations

6,450,921

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

36aa4a6a71a9b48a1867f8a3d4ef5922510e46218aca57c7198298e9aff925e8

Transactions (2)

Coinbase5a39e8d1f9d7f4…a48108c7e9fcf0

1 in → 27 out9.1695 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz

815d6387bf03e6…91fd9cab96abed

1 in → 2 out187.5388 XPM226 B

AVetKTkQ…u9vorqam APRooyyB…j6Kw1g9L

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.

3.064 × 10⁹⁵(96-digit number)

30647120618035149094…52560973596395263999

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

3.064 × 10⁹⁵(96-digit number)

30647120618035149094…52560973596395263999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.064 × 10⁹⁵(96-digit number)

30647120618035149094…52560973596395264001

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

6.129 × 10⁹⁵(96-digit number)

61294241236070298188…05121947192790527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.129 × 10⁹⁵(96-digit number)

61294241236070298188…05121947192790528001

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

1.225 × 10⁹⁶(97-digit number)

12258848247214059637…10243894385581055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.225 × 10⁹⁶(97-digit number)

12258848247214059637…10243894385581056001

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

2.451 × 10⁹⁶(97-digit number)

24517696494428119275…20487788771162111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.451 × 10⁹⁶(97-digit number)

24517696494428119275…20487788771162112001

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

4.903 × 10⁹⁶(97-digit number)

49035392988856238550…40975577542324223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.903 × 10⁹⁶(97-digit number)

49035392988856238550…40975577542324224001

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 #365,341

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