Block #114,569

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 5:42:45 AM · Difficulty 9.7399 · 6,700,494 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c230dbf2a961743fde0ec00608a1eb734e4c251e29f06f3671634f9b9719c7cb

View on Chainz ↗

Height

#114,569

Difficulty

9.739916

Transactions

Size

428 B

Version

Bits

09bd6b26

Nonce

314

Timestamp

8/13/2013, 5:42:45 AM

Confirmations

6,700,494

Mined by

⛏️ P2SHAGZLHkuNvLfCawea6iQo8M9ytzWS2GBGrR

Merkle Root

6f29a5c7b7ed6436674c0f62c94a5a6311688cd5f463f2e44c19a02e31e1ead1

Transactions (2)

Coinbasecc1fdf753f52df…4b3794af56a3f9

1 in → 1 out10.5400 XPM110 B

AGZLHkuN…WS2GBGrR

08154b6e06e65a…425b3d1a453f66

1 in → 2 out4.1302 XPM226 B

ASNHooau…wTqh4E8T AUSNyBN5…VNtnaVkG

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.

2.929 × 10⁹⁸(99-digit number)

29299195554457226362…30384768180935570129

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

2.929 × 10⁹⁸(99-digit number)

29299195554457226362…30384768180935570129

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.929 × 10⁹⁸(99-digit number)

29299195554457226362…30384768180935570131

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

5.859 × 10⁹⁸(99-digit number)

58598391108914452724…60769536361871140259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.859 × 10⁹⁸(99-digit number)

58598391108914452724…60769536361871140261

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

1.171 × 10⁹⁹(100-digit number)

11719678221782890544…21539072723742280519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.171 × 10⁹⁹(100-digit number)

11719678221782890544…21539072723742280521

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

2.343 × 10⁹⁹(100-digit number)

23439356443565781089…43078145447484561039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.343 × 10⁹⁹(100-digit number)

23439356443565781089…43078145447484561041

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

4.687 × 10⁹⁹(100-digit number)

46878712887131562179…86156290894969122079

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 #114,569

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