Block #368,021

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 11:24:40 AM · Difficulty 10.4378 · 6,465,193 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

866166c713524d46987150bf00c557b24c0d0288d96f1ccb9ff583ded69d2953

View on Chainz ↗

Height

#368,021

Difficulty

10.437793

Transactions

Size

802 B

Version

Bits

0a70133a

Nonce

24,625

Timestamp

1/20/2014, 11:24:40 AM

Confirmations

6,465,193

Mined by

⛏️ P2SHAUBZH4esHffUJ4NuEw2FbocicJGB5GJd89

Merkle Root

423cd11bd8aa5bcdfd8aa9e61c801c7d04e5a7fd070067312132567bc87ba969

Transactions (3)

Coinbase0c5bbf38a5907c…becea1b09219ba

1 in → 1 out9.1800 XPM109 B

AUBZH4es…GB5GJd89

ac85a9b7e7ecc7…68b6677211651d

1 in → 2 out3.5866 XPM226 B

AG6MWU9b…mwigFNJg AazxGwTM…eVJEGqqt

c39421f03f67ad…33e77582010413

2 in → 2 out5.0567 XPM375 B

ATYBTDCF…jiCgMy5o AFreewNR…WwhUuhEf

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.

3.636 × 10⁹⁹(100-digit number)

36363469688713309299…75113860262768926719

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

3.636 × 10⁹⁹(100-digit number)

36363469688713309299…75113860262768926719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.636 × 10⁹⁹(100-digit number)

36363469688713309299…75113860262768926721

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

7.272 × 10⁹⁹(100-digit number)

72726939377426618599…50227720525537853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.272 × 10⁹⁹(100-digit number)

72726939377426618599…50227720525537853441

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

1.454 × 10¹⁰⁰(101-digit number)

14545387875485323719…00455441051075706879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.454 × 10¹⁰⁰(101-digit number)

14545387875485323719…00455441051075706881

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

2.909 × 10¹⁰⁰(101-digit number)

29090775750970647439…00910882102151413759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.909 × 10¹⁰⁰(101-digit number)

29090775750970647439…00910882102151413761

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

5.818 × 10¹⁰⁰(101-digit number)

58181551501941294879…01821764204302827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.818 × 10¹⁰⁰(101-digit number)

58181551501941294879…01821764204302827521

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 #368,021

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