Block #115,466

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 7:09:21 PM · Difficulty 9.7445 · 6,701,892 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d766e206787c25e54a5143b59b40c529c2a57d3e50c7353adc9e0860fc336259

View on Chainz ↗

Height

#115,466

Difficulty

9.744523

Transactions

Size

871 B

Version

Bits

09be9913

Nonce

5,375

Timestamp

8/13/2013, 7:09:21 PM

Confirmations

6,701,892

Mined by

⛏️ P2SHAGXS5BR4JtM3bWKHEDBi3oNEr4WtNUVc3H

Merkle Root

a11ff1d1074fc2f4615c13dfcec285b93b4ee831aff54366cb0d642dce8e7e2f

Transactions (2)

Coinbase71adf1425f7bfa…b34d91948ee41f

1 in → 1 out10.5300 XPM109 B

AGXS5BR4…WtNUVc3H

bcfc64d2d64681…40d8d97de986e2

4 in → 2 out377.4663 XPM670 B

AZ18dHbE…RuNBWmPo AUrFcvbc…rG6gxnPP

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.

1.781 × 10⁹⁸(99-digit number)

17810442209421791839…30932538237466568569

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

1.781 × 10⁹⁸(99-digit number)

17810442209421791839…30932538237466568569

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.781 × 10⁹⁸(99-digit number)

17810442209421791839…30932538237466568571

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

3.562 × 10⁹⁸(99-digit number)

35620884418843583678…61865076474933137139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.562 × 10⁹⁸(99-digit number)

35620884418843583678…61865076474933137141

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

7.124 × 10⁹⁸(99-digit number)

71241768837687167357…23730152949866274279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.124 × 10⁹⁸(99-digit number)

71241768837687167357…23730152949866274281

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

1.424 × 10⁹⁹(100-digit number)

14248353767537433471…47460305899732548559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.424 × 10⁹⁹(100-digit number)

14248353767537433471…47460305899732548561

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

2.849 × 10⁹⁹(100-digit number)

28496707535074866942…94920611799465097119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 #115,466

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