Block #3,667,863

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2020, 10:02:44 AM · Difficulty 10.8844 · 3,148,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88e7dedc1067dda5be07d2471501e6bdbe60bc6d80a4bbcbad056ea7d3ebc1be

View on Chainz ↗

Height

#3,667,863

Difficulty

10.884413

Transactions

Size

3.34 KB

Version

Bits

0ae268df

Nonce

992,200,415

Timestamp

5/2/2020, 10:02:44 AM

Confirmations

3,148,564

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

8651e692b0686c50e71005389e5444118cd6955ddf8acda6a5e4556fa5c7a510

Transactions (5)

Coinbasede3af05d7bbc4e…68bc8216ab146d

1 in → 1 out8.4900 XPM110 B

ASiq2qtK…VMhmk7yL

46075a5584fb18…7525200b55d279

12 in → 2 out101.1400 XPM1.41 KB

ASiq2qtK…VMhmk7yL AW4mGrtW…iwgXpKbG

2723a970f709bd…de52ac5795d8ff

5 in → 2 out42.1400 XPM648 B

ASiq2qtK…VMhmk7yL AcLxmubQ…zPqUHd8P

734a448375a936…86dbad6b412eb7

2 in → 2 out11.1768 XPM341 B

AHpNx8Vr…ekfk1EFW ASiq2qtK…VMhmk7yL

a9c4c4e83ac68c…3e5eeb649e8e30

5 in → 2 out10.1011 XPM785 B

ASiq2qtK…VMhmk7yL AWxHVeWs…Q7RMs542

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.

1.078 × 10⁹⁹(100-digit number)

10784233807616670097…65930415776632831999

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

1.078 × 10⁹⁹(100-digit number)

10784233807616670097…65930415776632831999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.078 × 10⁹⁹(100-digit number)

10784233807616670097…65930415776632832001

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

2.156 × 10⁹⁹(100-digit number)

21568467615233340195…31860831553265663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.156 × 10⁹⁹(100-digit number)

21568467615233340195…31860831553265664001

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

4.313 × 10⁹⁹(100-digit number)

43136935230466680390…63721663106531327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.313 × 10⁹⁹(100-digit number)

43136935230466680390…63721663106531328001

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

8.627 × 10⁹⁹(100-digit number)

86273870460933360781…27443326213062655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.627 × 10⁹⁹(100-digit number)

86273870460933360781…27443326213062656001

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

1.725 × 10¹⁰⁰(101-digit number)

17254774092186672156…54886652426125311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.725 × 10¹⁰⁰(101-digit number)

17254774092186672156…54886652426125312001

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 #3,667,863

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