Block #9,745

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 12:07:49 AM · Difficulty 7.6361 · 6,779,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47651593e0843207c6f80508fc4120d365400ceb12ecf53e524ab6e06e80baad

View on Chainz ↗

Height

#9,745

Difficulty

7.636056

Transactions

Size

984 B

Version

Bits

07a2d499

Nonce

1,177

Timestamp

7/11/2013, 12:07:49 AM

Confirmations

6,779,330

Merkle Root

049d5196b5aba0c3df1ce70876079955d198f8f1763d327fe496a06484ea9ecb

Transactions (2)

Coinbaseee300736cd4b90…265a02df552446

1 in → 1 out17.1600 XPM108 B

APLhVYm2…nE7HzNK8

8ccdb381b9c946…6823a4ef328ebd

5 in → 1 out1020.4000 XPM782 B

AWbfM7mC…jLoqqkiU

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.

2.356 × 10¹⁰⁵(106-digit number)

23561285879776197183…80274189434400613199

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

2.356 × 10¹⁰⁵(106-digit number)

23561285879776197183…80274189434400613199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.356 × 10¹⁰⁵(106-digit number)

23561285879776197183…80274189434400613201

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

4.712 × 10¹⁰⁵(106-digit number)

47122571759552394366…60548378868801226399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.712 × 10¹⁰⁵(106-digit number)

47122571759552394366…60548378868801226401

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

9.424 × 10¹⁰⁵(106-digit number)

94245143519104788733…21096757737602452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.424 × 10¹⁰⁵(106-digit number)

94245143519104788733…21096757737602452801

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

1.884 × 10¹⁰⁶(107-digit number)

18849028703820957746…42193515475204905599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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