Block #1,678,856

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/18/2016, 6:54:20 PM · Difficulty 10.6967 · 5,130,121 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43a7a04ad52e77453fc82cecf37994de4afba51b69a342783f98d4b7e583cc4c

View on Chainz ↗

Height

#1,678,856

Difficulty

10.696668

Transactions

Size

2.19 KB

Version

Bits

0ab258da

Nonce

1,215,986,425

Timestamp

7/18/2016, 6:54:20 PM

Confirmations

5,130,121

Mined by

⛏️ P2SHAJ4yuRPXjwHEh2zigjQfN7WbgVR4bEu1yU

Merkle Root

3ef1d5b4aae22cd8a337596ea102cc69ce3c592f1e3b83fa1675c1a5fcbd1c83

Transactions (2)

Coinbased20baacff473d1…b18f5c9b286627

1 in → 1 out8.7600 XPM110 B

AJ4yuRPX…R4bEu1yU

7856c3d2e62847…01b87d4593211e

2 in → 51 out17.7184 XPM1.99 KB

AcPt5wua…cv6rG7Cw ASqHeCEh…JeERkaMp ANU9YUmT…LVVRpe4K AT2hZpt5…ygN5oMvw ALT3rMFM…onee4aCd

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.

3.120 × 10⁹⁴(95-digit number)

31207956695977561617…80890329705817361359

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

3.120 × 10⁹⁴(95-digit number)

31207956695977561617…80890329705817361359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.120 × 10⁹⁴(95-digit number)

31207956695977561617…80890329705817361361

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

6.241 × 10⁹⁴(95-digit number)

62415913391955123234…61780659411634722719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.241 × 10⁹⁴(95-digit number)

62415913391955123234…61780659411634722721

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

1.248 × 10⁹⁵(96-digit number)

12483182678391024646…23561318823269445439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.248 × 10⁹⁵(96-digit number)

12483182678391024646…23561318823269445441

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

2.496 × 10⁹⁵(96-digit number)

24966365356782049293…47122637646538890879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.496 × 10⁹⁵(96-digit number)

24966365356782049293…47122637646538890881

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

4.993 × 10⁹⁵(96-digit number)

49932730713564098587…94245275293077781759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.993 × 10⁹⁵(96-digit number)

49932730713564098587…94245275293077781761

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 #1,678,856

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