Block #384,620

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 6:12:00 AM · Difficulty 10.4000 · 6,429,611 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2f3f285e16116cf1b520bc3582a16a2dd6fabd2e928204db037375b685dba27

View on Chainz ↗

Height

#384,620

Difficulty

10.400039

Transactions

Size

1.47 KB

Version

Bits

0a6668f2

Nonce

64,087

Timestamp

2/1/2014, 6:12:00 AM

Confirmations

6,429,611

Mined by

⛏️ laR{AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5c2b5b2b17a0660517b3775c7fbec7d5cd63fd5c33eec1eecbacdb3d6f077a87

Transactions (4)

Coinbase864cb0196237af…12adc48e74f65f

1 in → 20 out9.2300 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AZEjFnfh…BQPptrcw

48c56f5e87d286…0493e57ac5bc10

1 in → 2 out6.1318 XPM225 B

APuytmwy…RaGFt9Tk AQrAppYf…pmUyxgj9

7a48dac8ad3788…89fe300b1e1903

1 in → 2 out5.0751 XPM225 B

ALCjshBK…CRCCzTpm APWMuLLh…WmRbbPbb

e068d072118148…66448dbab94131

1 in → 2 out2.0531 XPM226 B

AdDtPVgp…jAug6bCk Ads74aaq…fLmXA4Np

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.

4.124 × 10⁹²(93-digit number)

41243717618662338995…88364515642702902479

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

4.124 × 10⁹²(93-digit number)

41243717618662338995…88364515642702902479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.124 × 10⁹²(93-digit number)

41243717618662338995…88364515642702902481

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

8.248 × 10⁹²(93-digit number)

82487435237324677991…76729031285405804959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.248 × 10⁹²(93-digit number)

82487435237324677991…76729031285405804961

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

1.649 × 10⁹³(94-digit number)

16497487047464935598…53458062570811609919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.649 × 10⁹³(94-digit number)

16497487047464935598…53458062570811609921

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

3.299 × 10⁹³(94-digit number)

32994974094929871196…06916125141623219839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.299 × 10⁹³(94-digit number)

32994974094929871196…06916125141623219841

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

6.598 × 10⁹³(94-digit number)

65989948189859742393…13832250283246439679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.598 × 10⁹³(94-digit number)

65989948189859742393…13832250283246439681

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 #384,620

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