Block #2,807,829

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/24/2018, 10:52:28 AM · Difficulty 11.6724 · 4,035,535 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5468f1fb63298a669f5640e344cca99c0749c6ec792b36ce528b8e78e19455af

View on Chainz ↗

Height

#2,807,829

Difficulty

11.672448

Transactions

Size

1.72 KB

Version

Bits

0bac258c

Nonce

1,543,075,600

Timestamp

8/24/2018, 10:52:28 AM

Confirmations

4,035,535

Mined by

⛏️ P2SHAd9Pnv2QzErL2y6SNF51iCmoHGkjWRKGKF

Merkle Root

c36285e1fb654818e813004d097187082ba0dd59fd4692f238599ca188f5ab84

Transactions (2)

Coinbase3e8f4c97fc51e2…b31aadbc6082a4

1 in → 1 out7.3500 XPM110 B

Ad9Pnv2Q…kjWRKGKF

9b6d636865f81b…01845461aae8d3

10 in → 2 out36.0600 XPM1.52 KB

AKqCXWsM…Gei1SLtq AQRn6yfR…z5FsKtdj

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.

9.864 × 10⁹⁶(97-digit number)

98646419043364697682…26275923782381649919

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

9.864 × 10⁹⁶(97-digit number)

98646419043364697682…26275923782381649919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.864 × 10⁹⁶(97-digit number)

98646419043364697682…26275923782381649921

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

1.972 × 10⁹⁷(98-digit number)

19729283808672939536…52551847564763299839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.972 × 10⁹⁷(98-digit number)

19729283808672939536…52551847564763299841

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

3.945 × 10⁹⁷(98-digit number)

39458567617345879073…05103695129526599679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.945 × 10⁹⁷(98-digit number)

39458567617345879073…05103695129526599681

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

7.891 × 10⁹⁷(98-digit number)

78917135234691758146…10207390259053199359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.891 × 10⁹⁷(98-digit number)

78917135234691758146…10207390259053199361

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

1.578 × 10⁹⁸(99-digit number)

15783427046938351629…20414780518106398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.578 × 10⁹⁸(99-digit number)

15783427046938351629…20414780518106398721

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

3.156 × 10⁹⁸(99-digit number)

31566854093876703258…40829561036212797439

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 #2,807,829

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