Block #46,388

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 6:21:00 AM · Difficulty 8.7905 · 6,758,997 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5d35e7e9c018e5f41507696bfae91d7b2fb448f34997cab2b25a5a6a7067f35

View on Chainz ↗

Height

#46,388

Difficulty

8.790503

Transactions

Size

509 B

Version

Bits

08ca5e6b

Nonce

641

Timestamp

7/15/2013, 6:21:00 AM

Confirmations

6,758,997

Mined by

⛏️ P2SHAJkys6Q5wwS95mwDSxeonBU729hVcoruvt

Merkle Root

88c9c99c92ea94b03c505c1a8940dc33e90fb50b883e830d06dcfaff2b0adcf0

Transactions (2)

Coinbase0c7decb8034c7f…74537abe019ceb

1 in → 1 out12.9300 XPM109 B

AJkys6Q5…hVcoruvt

749fd9ab2d80d4…a76346dc5ce755

2 in → 1 out13.5200 XPM306 B

AScNu17i…EEtEnKS9

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.

1.157 × 10¹⁰⁵(106-digit number)

11576080603255616895…73047280693375964219

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

1.157 × 10¹⁰⁵(106-digit number)

11576080603255616895…73047280693375964219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.157 × 10¹⁰⁵(106-digit number)

11576080603255616895…73047280693375964221

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

2.315 × 10¹⁰⁵(106-digit number)

23152161206511233791…46094561386751928439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.315 × 10¹⁰⁵(106-digit number)

23152161206511233791…46094561386751928441

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

4.630 × 10¹⁰⁵(106-digit number)

46304322413022467582…92189122773503856879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.630 × 10¹⁰⁵(106-digit number)

46304322413022467582…92189122773503856881

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

9.260 × 10¹⁰⁵(106-digit number)

92608644826044935165…84378245547007713759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.260 × 10¹⁰⁵(106-digit number)

92608644826044935165…84378245547007713761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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