Block #66,341

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 4:58:08 PM · Difficulty 8.9860 · 6,740,030 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

369b0b5f10591695d266dc1383c10f7abb4cc85e825657f1c3426cb9736a33ac

View on Chainz ↗

Height

#66,341

Difficulty

8.985993

Transactions

Size

1.27 KB

Version

Bits

08fc6a04

Nonce

596

Timestamp

7/19/2013, 4:58:08 PM

Confirmations

6,740,030

Mined by

⛏️ P2SHAK54ZH9oxvy1huabbh1u957ndfet3mJV5x

Merkle Root

7d76e6c253298d686726402d021b7d0d7af284d595909b46075a1387b890ce44

Transactions (3)

Coinbase0a937b8d31aa6f…ca247581589b58

1 in → 1 out12.3900 XPM110 B

AK54ZH9o…et3mJV5x

845bb867c5c761…d0d22c30ac691e

6 in → 1 out112.7400 XPM727 B

AU1zMWV4…Skyd7sgs

a93fda49208a1e…752ec1050ab25d

2 in → 2 out147.6500 XPM375 B

AeEMZMPH…udUHn11X ATYAR5wH…PJWg8dG9

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.

8.304 × 10¹⁰¹(102-digit number)

83043480044102846480…91293933049672252249

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

8.304 × 10¹⁰¹(102-digit number)

83043480044102846480…91293933049672252249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.304 × 10¹⁰¹(102-digit number)

83043480044102846480…91293933049672252251

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

1.660 × 10¹⁰²(103-digit number)

16608696008820569296…82587866099344504499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.660 × 10¹⁰²(103-digit number)

16608696008820569296…82587866099344504501

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

3.321 × 10¹⁰²(103-digit number)

33217392017641138592…65175732198689008999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.321 × 10¹⁰²(103-digit number)

33217392017641138592…65175732198689009001

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

6.643 × 10¹⁰²(103-digit number)

66434784035282277184…30351464397378017999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.643 × 10¹⁰²(103-digit number)

66434784035282277184…30351464397378018001

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

Block #66,341

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