Block #397,081

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 8:15:35 PM · Difficulty 10.4157 · 6,410,412 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3aaa325ab301ae594fa54d337d565c65a088389d9311155210c897ccfeb5ea6

View on Chainz ↗

Height

#397,081

Difficulty

10.415686

Transactions

Size

1.08 KB

Version

Bits

0a6a6a6b

Nonce

64,587

Timestamp

2/9/2014, 8:15:35 PM

Confirmations

6,410,412

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d37447d4f5bfb699a5eeb38d91a5c877e3805813d4658cca9bbbeedc5ad31c2c

Transactions (5)

Coinbaseaea24f9d0c3b7e…299dfcdf341502

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

b0cea22fc2b5c5…dd85d8e788cc72

1 in → 2 out9.1600 XPM226 B

ATsxPu1m…TA97EVfr AS9byuV8…vAjBsXQ6

3ca7efc7bbdc33…6b52a06e21317e

1 in → 2 out8.1480 XPM226 B

Ae1fK6AT…xoJjUwaT AW4jmiGj…4nr8i2me

ae0675792c3220…e1e3503dd00a08

1 in → 2 out7.1333 XPM225 B

Ad3s9mx2…ivHrXQ5y AR5QEwtm…11EjdWVu

ece93811ec16ff…ad24c8a7351ac3

1 in → 2 out6.1005 XPM227 B

AXC8ek1T…8TLim3gV AKRsN9VK…FuatDCZ4

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.

2.148 × 10⁹⁹(100-digit number)

21486617404292660760…57608168438752634879

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

2.148 × 10⁹⁹(100-digit number)

21486617404292660760…57608168438752634879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.148 × 10⁹⁹(100-digit number)

21486617404292660760…57608168438752634881

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

4.297 × 10⁹⁹(100-digit number)

42973234808585321521…15216336877505269759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.297 × 10⁹⁹(100-digit number)

42973234808585321521…15216336877505269761

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

8.594 × 10⁹⁹(100-digit number)

85946469617170643043…30432673755010539519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.594 × 10⁹⁹(100-digit number)

85946469617170643043…30432673755010539521

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

1.718 × 10¹⁰⁰(101-digit number)

17189293923434128608…60865347510021079039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.718 × 10¹⁰⁰(101-digit number)

17189293923434128608…60865347510021079041

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

3.437 × 10¹⁰⁰(101-digit number)

34378587846868257217…21730695020042158079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.437 × 10¹⁰⁰(101-digit number)

34378587846868257217…21730695020042158081

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 #397,081

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