Block #1,225,726

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2015, 9:06:41 AM · Difficulty 10.7357 · 5,592,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9295d45faecb337101a8c8c00802020a4ec7cff5c54914b8dab8c7d3d0753511

View on Chainz ↗

Height

#1,225,726

Difficulty

10.735723

Transactions

Size

1.72 KB

Version

Bits

0abc585a

Nonce

55,533,475

Timestamp

9/7/2015, 9:06:41 AM

Confirmations

5,592,015

Mined by

⛏️ P2SHAVTHDKEQ3bjGWMhNv8eZtVVfoeG4ZuKdSL

Merkle Root

22b01a48687fe51c479f08e4c33b5a3be524e7d70d1920c06525b9b928bff67e

Transactions (4)

Coinbase7ed126a4531b28…56eccfd3490c7a

1 in → 1 out8.6900 XPM110 B

AVTHDKEQ…G4ZuKdSL

6545f208fab11e…682537a16006fd

6 in → 2 out35.5941 XPM965 B

AJAt6F2F…pvn2uR8Z AUHemyvF…Fx8Y6FWZ

cc97cc634d58aa…bf32702904744b

2 in → 2 out15.2955 XPM372 B

AX552jX9…gDRZgjsX AGKxcm35…bTDCuXzY

51f22b69da3dfa…e40b403cd8754a

1 in → 2 out7.1625 XPM227 B

AGcTbKTW…x8qSsy2o AcEGUXDj…JsRzHiLU

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.

2.268 × 10⁹⁷(98-digit number)

22688751676406116709…61367725736380866559

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

2.268 × 10⁹⁷(98-digit number)

22688751676406116709…61367725736380866559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.268 × 10⁹⁷(98-digit number)

22688751676406116709…61367725736380866561

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

4.537 × 10⁹⁷(98-digit number)

45377503352812233418…22735451472761733119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.537 × 10⁹⁷(98-digit number)

45377503352812233418…22735451472761733121

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

9.075 × 10⁹⁷(98-digit number)

90755006705624466837…45470902945523466239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.075 × 10⁹⁷(98-digit number)

90755006705624466837…45470902945523466241

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

1.815 × 10⁹⁸(99-digit number)

18151001341124893367…90941805891046932479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.815 × 10⁹⁸(99-digit number)

18151001341124893367…90941805891046932481

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

3.630 × 10⁹⁸(99-digit number)

36302002682249786735…81883611782093864959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.630 × 10⁹⁸(99-digit number)

36302002682249786735…81883611782093864961

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 #1,225,726

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