Block #329,200

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 7:08:16 PM · Difficulty 10.1742 · 6,485,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0737c47498f10a6e7d773dfd2166d22b24163f215a413f889428ac4da66dbad8

View on Chainz ↗

Height

#329,200

Difficulty

10.174224

Transactions

Size

1.26 KB

Version

Bits

0a2c99f3

Nonce

269,632

Timestamp

12/25/2013, 7:08:16 PM

Confirmations

6,485,058

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

15060128786662fe619bd7cc306bbb98a078a3c44b28ea9854d06d0da11e8040

Transactions (4)

Coinbase808375bc7dd2d6…0b7cfb9860b5cf

1 in → 1 out9.6800 XPM110 B

AeKNrjNj…1NEq95Ta

1aaa4c70d5e675…ee059438310cc9

2 in → 2 out75.0100 XPM376 B

AbyGX1oS…zDGC2Ray ARmBJcFR…LitmiVbF

421ebf04273246…6c3e1df7ea0a88

3 in → 1 out6.9934 XPM489 B

ANLvnoNx…nCARZFi1

f28302565ad31f…de680c079f558a

1 in → 2 out2.9913 XPM226 B

ALuagM7p…CLrLri1h AadhYTPy…NkvKmcXG

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.

2.444 × 10¹⁰⁰(101-digit number)

24444052987607658187…87694498054602506239

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

2.444 × 10¹⁰⁰(101-digit number)

24444052987607658187…87694498054602506239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.444 × 10¹⁰⁰(101-digit number)

24444052987607658187…87694498054602506241

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

4.888 × 10¹⁰⁰(101-digit number)

48888105975215316375…75388996109205012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.888 × 10¹⁰⁰(101-digit number)

48888105975215316375…75388996109205012481

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

9.777 × 10¹⁰⁰(101-digit number)

97776211950430632751…50777992218410024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.777 × 10¹⁰⁰(101-digit number)

97776211950430632751…50777992218410024961

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

1.955 × 10¹⁰¹(102-digit number)

19555242390086126550…01555984436820049919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.955 × 10¹⁰¹(102-digit number)

19555242390086126550…01555984436820049921

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

3.911 × 10¹⁰¹(102-digit number)

39110484780172253100…03111968873640099839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.911 × 10¹⁰¹(102-digit number)

39110484780172253100…03111968873640099841

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 #329,200

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