Block #395,952

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 2:20:39 AM · Difficulty 10.4094 · 6,412,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3dcfce609efc3582dbf51e271f7178a1469bf8d75c741bd36cc9b1f410c9e02

View on Chainz ↗

Height

#395,952

Difficulty

10.409441

Transactions

Size

3.44 KB

Version

Bits

0a68d125

Nonce

318,693

Timestamp

2/9/2014, 2:20:39 AM

Confirmations

6,412,186

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

968b77e093e4eb5a0c1bafdd896b5b966d67ec248f405783653ef57c6cbddc0b

Transactions (5)

Coinbasee310b6323e42b0…5627310c3c14c6

1 in → 1 out9.2771 XPM110 B

AeKNrjNj…1NEq95Ta

9585832b5ae665…9180828a3a03c2

18 in → 1 out25.0200 XPM2.64 KB

AVduR1E6…ZAqsBqXe

348fa76825cde2…436d200e112459

1 in → 1 out9.1800 XPM157 B

AJjEKveq…Ldtq9FLd

f978ce16a27427…e1770a68d70c73

1 in → 2 out9.1500 XPM226 B

ANXVBknh…yBvt6Z1U AGUjUX5P…L3bBAhtF

f156f6ae58778c…10c809ca8dc14a

1 in → 2 out8.1355 XPM225 B

AXopUYfB…nsdx6xRW APS7ShEa…HPEvLkkb

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.

3.469 × 10¹⁰⁵(106-digit number)

34693026848523547279…93420064537171630079

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

3.469 × 10¹⁰⁵(106-digit number)

34693026848523547279…93420064537171630079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.469 × 10¹⁰⁵(106-digit number)

34693026848523547279…93420064537171630081

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

6.938 × 10¹⁰⁵(106-digit number)

69386053697047094559…86840129074343260159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.938 × 10¹⁰⁵(106-digit number)

69386053697047094559…86840129074343260161

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

1.387 × 10¹⁰⁶(107-digit number)

13877210739409418911…73680258148686520319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.387 × 10¹⁰⁶(107-digit number)

13877210739409418911…73680258148686520321

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

2.775 × 10¹⁰⁶(107-digit number)

27754421478818837823…47360516297373040639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.775 × 10¹⁰⁶(107-digit number)

27754421478818837823…47360516297373040641

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

5.550 × 10¹⁰⁶(107-digit number)

55508842957637675647…94721032594746081279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.550 × 10¹⁰⁶(107-digit number)

55508842957637675647…94721032594746081281

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 #395,952

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