Block #398,160

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 1:28:53 PM · Difficulty 10.4214 · 6,419,628 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7aade36a700e9a58d0926bbc405f2b71b89d22880e359c081089e955e74cb6c8

View on Chainz ↗

Height

#398,160

Difficulty

10.421439

Transactions

Size

1.80 KB

Version

Bits

0a6be365

Nonce

43,999

Timestamp

2/10/2014, 1:28:53 PM

Confirmations

6,419,628

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ec1bc482d28ae9088a99abbd61e6229429511839d0c3fb2f1810d293d3e4cbe3

Transactions (5)

Coinbased6307ddc3c7a9e…bbf98e65a3ffa6

1 in → 1 out9.2300 XPM109 B

AeKNrjNj…1NEq95Ta

69063971e173ed…20ddfc31017a33

2 in → 2 out10.3502 XPM374 B

AQ5qntoJ…N8Uwc7Px AJhgf59P…W42GoeAR

35bfdae9031828…314260a65b7bfa

4 in → 2 out25.0517 XPM669 B

Abxn3EEB…8ccf7zVj AaY7Sg5f…ygWKLvmr

e5fdd6c915c3c8…72e08dfb590e80

2 in → 2 out3.3456 XPM374 B

AP7MBQyR…YC7pYu93 AcmZKonK…R2Du8pP8

59bbd425589d9c…6cd91ca2996a96

1 in → 2 out2.1372 XPM226 B

AGqGfq1N…djdc3DmQ AW9eU7kW…QvVS27oZ

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.

4.081 × 10⁹⁹(100-digit number)

40815615236414506804…92951702639846666879

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

4.081 × 10⁹⁹(100-digit number)

40815615236414506804…92951702639846666879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.081 × 10⁹⁹(100-digit number)

40815615236414506804…92951702639846666881

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

8.163 × 10⁹⁹(100-digit number)

81631230472829013608…85903405279693333759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.163 × 10⁹⁹(100-digit number)

81631230472829013608…85903405279693333761

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

1.632 × 10¹⁰⁰(101-digit number)

16326246094565802721…71806810559386667519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.632 × 10¹⁰⁰(101-digit number)

16326246094565802721…71806810559386667521

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

3.265 × 10¹⁰⁰(101-digit number)

32652492189131605443…43613621118773335039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.265 × 10¹⁰⁰(101-digit number)

32652492189131605443…43613621118773335041

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

6.530 × 10¹⁰⁰(101-digit number)

65304984378263210887…87227242237546670079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.530 × 10¹⁰⁰(101-digit number)

65304984378263210887…87227242237546670081

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 #398,160

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