Block #685,043

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/20/2014, 11:38:20 AM · Difficulty 10.9562 · 6,109,321 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ebeff0fa4e760854631331e5bfe7ad7bd9ce3489c09ed39f785a3ce1bc631d2

View on Chainz ↗

Height

#685,043

Difficulty

10.956236

Transactions

Size

1.23 KB

Version

Bits

0af4cbe1

Nonce

600,898,021

Timestamp

8/20/2014, 11:38:20 AM

Confirmations

6,109,321

Merkle Root

a95f127e39d355f76b86e26439a9855225e495493fb30c663d3a574b6c272688

Transactions (5)

Coinbase4d0734bf5d6101…0bd84138c29839

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

73277a07cb7126…6f0c775d9a8101

1 in → 2 out8.2900 XPM227 B

ASx9RPHT…8fVzc2Ey AMmCzrgg…2W3ExKMo

7bccc2665bf25d…8806c8ea24fd5a

1 in → 3 out8.3000 XPM227 B

AeKNrjNj…1NEq95Ta AHCuz9P2…41tUcRdy AKinBSz6…c5jHh6RZ

910afe7f71f3da…6198035cd2e446

2 in → 2 out5.3137 XPM375 B

AYrwBKyU…1S6w2wRP AUzyWwZU…mT96QcTz

823c73795c744f…4cb61c176ebf74

1 in → 2 out1.5514 XPM226 B

ASrYeiHQ…GZsXQfSy AW2zddGZ…EgxdA4th

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.

7.268 × 10⁹⁷(98-digit number)

72683220951819754336…17867706202776683519

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

7.268 × 10⁹⁷(98-digit number)

72683220951819754336…17867706202776683519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.268 × 10⁹⁷(98-digit number)

72683220951819754336…17867706202776683521

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

1.453 × 10⁹⁸(99-digit number)

14536644190363950867…35735412405553367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.453 × 10⁹⁸(99-digit number)

14536644190363950867…35735412405553367041

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

2.907 × 10⁹⁸(99-digit number)

29073288380727901734…71470824811106734079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.907 × 10⁹⁸(99-digit number)

29073288380727901734…71470824811106734081

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

5.814 × 10⁹⁸(99-digit number)

58146576761455803469…42941649622213468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.814 × 10⁹⁸(99-digit number)

58146576761455803469…42941649622213468161

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

1.162 × 10⁹⁹(100-digit number)

11629315352291160693…85883299244426936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.162 × 10⁹⁹(100-digit number)

11629315352291160693…85883299244426936321

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

2.325 × 10⁹⁹(100-digit number)

23258630704582321387…71766598488853872639

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