Block #422,347

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 3:50:35 PM · Difficulty 10.3805 · 6,391,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6448051abf402e34f90469b6a137fcedea94aef513673a1d6c85f634aafebf8

View on Chainz ↗

Height

#422,347

Difficulty

10.380528

Transactions

Size

1.17 KB

Version

Bits

0a616a48

Nonce

47,733

Timestamp

2/27/2014, 3:50:35 PM

Confirmations

6,391,580

Mined by

⛏️ qaS_AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ca4912dde85bb90d1ded9baeac725b9bc6bd2b3b7a90e91c99ffcc4edd3c58e9

Transactions (2)

Coinbasea2a070e5c40ece…abb49a08792278

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AMSvYdDV…AM3cN4zw

9901a704c12474…6b49635a6084cc

1 in → 2 out3.1185 XPM226 B

AMiVTMtt…4Knq1ve9 AUyBiqZh…x3MpWyjK

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.

3.054 × 10⁹³(94-digit number)

30541960615941170140…27919948491055133549

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

3.054 × 10⁹³(94-digit number)

30541960615941170140…27919948491055133549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.054 × 10⁹³(94-digit number)

30541960615941170140…27919948491055133551

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

6.108 × 10⁹³(94-digit number)

61083921231882340281…55839896982110267099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.108 × 10⁹³(94-digit number)

61083921231882340281…55839896982110267101

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

1.221 × 10⁹⁴(95-digit number)

12216784246376468056…11679793964220534199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.221 × 10⁹⁴(95-digit number)

12216784246376468056…11679793964220534201

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

2.443 × 10⁹⁴(95-digit number)

24433568492752936112…23359587928441068399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.443 × 10⁹⁴(95-digit number)

24433568492752936112…23359587928441068401

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

4.886 × 10⁹⁴(95-digit number)

48867136985505872224…46719175856882136799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.886 × 10⁹⁴(95-digit number)

48867136985505872224…46719175856882136801

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 #422,347

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