Block #422,193

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 1:20:58 PM · Difficulty 10.3803 · 6,377,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bed0c3c6ba4d8c58791f358d576ea9648392ab93674e1b1bb033be6c5e1cd093

View on Chainz ↗

Height

#422,193

Difficulty

10.380284

Transactions

Size

1.10 KB

Version

Bits

0a615a4f

Nonce

127,943

Timestamp

2/27/2014, 1:20:58 PM

Confirmations

6,377,061

Mined by

⛏️ 1qa<AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

5574e3ee47fb3752b222420e03a69a38a01c23c2960d5ead4afed54460313aa5

Transactions (5)

Coinbase15d6955d295524…131e6c987e38a6

1 in → 2 out9.3100 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

cb942b0d959f4c…079521a638111e

1 in → 2 out9.2000 XPM226 B

AGUH363b…udi75BeF AP5mpb7q…AvwsEUA3

a4587814330241…7acadd8994d93a

1 in → 2 out8.1892 XPM226 B

AQmP5faD…jdjNT11D AHksUkWQ…geieEwPK

a1df8d8b3ecacb…98a537ef62119d

1 in → 2 out5.1545 XPM226 B

AadgMcZP…jYenMnQF AMTu44Lk…J9mNj5Pg

847104e403bde1…b1c077e4d87ec8

1 in → 2 out5.0858 XPM226 B

AXh1JM6o…QjNr6wN2 AcmCDb8p…on2DWkGG

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.

3.666 × 10⁹⁸(99-digit number)

36662103867153675642…34049747827800983039

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

3.666 × 10⁹⁸(99-digit number)

36662103867153675642…34049747827800983039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.666 × 10⁹⁸(99-digit number)

36662103867153675642…34049747827800983041

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

7.332 × 10⁹⁸(99-digit number)

73324207734307351285…68099495655601966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.332 × 10⁹⁸(99-digit number)

73324207734307351285…68099495655601966081

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

1.466 × 10⁹⁹(100-digit number)

14664841546861470257…36198991311203932159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.466 × 10⁹⁹(100-digit number)

14664841546861470257…36198991311203932161

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

2.932 × 10⁹⁹(100-digit number)

29329683093722940514…72397982622407864319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.932 × 10⁹⁹(100-digit number)

29329683093722940514…72397982622407864321

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

5.865 × 10⁹⁹(100-digit number)

58659366187445881028…44795965244815728639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.865 × 10⁹⁹(100-digit number)

58659366187445881028…44795965244815728641

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