Block #43,201

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 8:24:15 PM · Difficulty 8.6496 · 6,746,638 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

feed39752ec87321517188651c59f5692666476f616b8f5cc603cdce54787b93

View on Chainz ↗

Height

#43,201

Difficulty

8.649647

Transactions

Size

7.52 KB

Version

Bits

08a64f45

Nonce

238

Timestamp

7/14/2013, 8:24:15 PM

Confirmations

6,746,638

Merkle Root

f562597d754bd813737fa5bd734a4d3b3e39039ae7a4430c3a969b55e2e6798d

Transactions (3)

Coinbase41b4f7d3d276d4…f2bd95b5574db2

1 in → 1 out13.4300 XPM110 B

AVd5yTMP…kSMcaW6D

ac57000610a881…ba98aeb75dd0d1

32 in → 1 out500.0000 XPM3.60 KB

AduwKP5J…wp1LyLxL

a792839f9524a5…6dbd35675d8451

33 in → 1 out500.0000 XPM3.72 KB

ANBGBvzR…CgPGtqfX

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.

4.833 × 10⁹⁶(97-digit number)

48333657883992479763…99060844568285636979

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

4.833 × 10⁹⁶(97-digit number)

48333657883992479763…99060844568285636979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.833 × 10⁹⁶(97-digit number)

48333657883992479763…99060844568285636981

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

9.666 × 10⁹⁶(97-digit number)

96667315767984959526…98121689136571273959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.666 × 10⁹⁶(97-digit number)

96667315767984959526…98121689136571273961

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

1.933 × 10⁹⁷(98-digit number)

19333463153596991905…96243378273142547919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.933 × 10⁹⁷(98-digit number)

19333463153596991905…96243378273142547921

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

3.866 × 10⁹⁷(98-digit number)

38666926307193983810…92486756546285095839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.866 × 10⁹⁷(98-digit number)

38666926307193983810…92486756546285095841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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