Block #399,550

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 12:05:22 PM · Difficulty 10.4257 · 6,402,089 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9b67c0cb18ace8ed94c60934fa6c75a25f2950ea72c15d369b09fd253399a30

View on Chainz ↗

Height

#399,550

Difficulty

10.425749

Transactions

Size

1.61 KB

Version

Bits

0a6cfdea

Nonce

9,304

Timestamp

2/11/2014, 12:05:22 PM

Confirmations

6,402,089

Mined by

⛏️ vAcgDwGo8ZBUgEksBhbzKTxBsGWBBFwbjVo

Merkle Root

77927d78590e49d0cf0de60031347d1b23ff784568e3bda95276db57afc876d5

Transactions (4)

Coinbase5636324d7fe888…e855712e12f9f2

1 in → 25 out9.2204 XPM913 B

AcgDwGo8…BBFwbjVo AUzEPJFG…kYkA5U9V APJPNQaM…8nyTxzkW AU9n4fVh…kUqmhbCv ATp4jJhs…TbSgR8Qb

6186d75b3cb6b8…4107c1ef406056

1 in → 1 out0.9900 XPM193 B

ATcQSuFm…gHDbW9XZ

3735ed49990c05…a35afd133e5024

1 in → 2 out3.1065 XPM226 B

AXdEotsB…4dWA1B5P AMU8nEj9…Eo32pqxr

ed5492faf714b2…9b804b385cfc67

1 in → 2 out2.7656 XPM226 B

AKrWb6ue…sVNhh1CF Aa2BYSsf…zWKTnX1i

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.

1.213 × 10⁹⁶(97-digit number)

12135948410773707681…03196078125574809599

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

1.213 × 10⁹⁶(97-digit number)

12135948410773707681…03196078125574809599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.213 × 10⁹⁶(97-digit number)

12135948410773707681…03196078125574809601

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

2.427 × 10⁹⁶(97-digit number)

24271896821547415363…06392156251149619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.427 × 10⁹⁶(97-digit number)

24271896821547415363…06392156251149619201

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

4.854 × 10⁹⁶(97-digit number)

48543793643094830727…12784312502299238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.854 × 10⁹⁶(97-digit number)

48543793643094830727…12784312502299238401

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

9.708 × 10⁹⁶(97-digit number)

97087587286189661454…25568625004598476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.708 × 10⁹⁶(97-digit number)

97087587286189661454…25568625004598476801

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

1.941 × 10⁹⁷(98-digit number)

19417517457237932290…51137250009196953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.941 × 10⁹⁷(98-digit number)

19417517457237932290…51137250009196953601

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