Block #2,644,499

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 12:54:50 PM · Difficulty 11.7105 · 4,192,019 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5afd0758960f077f57c4d3f9c9b94e6f84e8b5051398883a4392875e037ea48

View on Chainz ↗

Height

#2,644,499

Difficulty

11.710464

Transactions

Size

202 B

Version

Bits

0bb5e0f2

Nonce

93,223,270

Timestamp

5/2/2018, 12:54:50 PM

Confirmations

4,192,019

Mined by

⛏️ P2SHAdov8wnmZ2w9c3s58h8KbJ2xmNYkjXH3eA

Merkle Root

018c0d497e1035ae3ce4102cf29a8953ce3f099aaa48ea9f8b925913ad935990

Transactions (1)

Coinbase018c0d497e1035…925913ad935990

1 in → 1 out7.2800 XPM110 B

Adov8wnm…YkjXH3eA

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.

7.554 × 10⁹⁹(100-digit number)

75540933489217113802…27202898656319897599

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

7.554 × 10⁹⁹(100-digit number)

75540933489217113802…27202898656319897599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.554 × 10⁹⁹(100-digit number)

75540933489217113802…27202898656319897601

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

1.510 × 10¹⁰⁰(101-digit number)

15108186697843422760…54405797312639795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.510 × 10¹⁰⁰(101-digit number)

15108186697843422760…54405797312639795201

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

3.021 × 10¹⁰⁰(101-digit number)

30216373395686845520…08811594625279590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.021 × 10¹⁰⁰(101-digit number)

30216373395686845520…08811594625279590401

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

6.043 × 10¹⁰⁰(101-digit number)

60432746791373691041…17623189250559180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.043 × 10¹⁰⁰(101-digit number)

60432746791373691041…17623189250559180801

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

1.208 × 10¹⁰¹(102-digit number)

12086549358274738208…35246378501118361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.208 × 10¹⁰¹(102-digit number)

12086549358274738208…35246378501118361601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.417 × 10¹⁰¹(102-digit number)

24173098716549476416…70492757002236723199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,644,499

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