Block #438,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 1:48:28 AM · Difficulty 10.3566 · 6,378,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8daf736d007018f6e8004d698e0c61378e1bb2ce568c1d94db6f56ea75bb0220

View on Chainz ↗

Height

#438,522

Difficulty

10.356591

Transactions

Size

820 B

Version

Bits

0a5b498c

Nonce

25,301

Timestamp

3/11/2014, 1:48:28 AM

Confirmations

6,378,233

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

aed3470d64db688adb0551f66b22c33e51f93fe6dc77614778bae9211ac0f432

Transactions (2)

Coinbase1e027e32ae3678…c16741a016d805

1 in → 1 out9.3200 XPM116 B

AbwWkWZt…kawDhufa

34534889ec7c37…72184a309b745f

2 in → 10 out10.8369 XPM610 B

AHpZVsQR…c5YYRgif AJ2yatY2…oxn1zmiJ AJ7bwxHw…vy276KPV AM67rT5F…RQ1YgZa4 ASefYTZD…V2rvP4JP

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.

1.629 × 10¹⁰⁵(106-digit number)

16297151831399925594…20568641244005009279

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

1.629 × 10¹⁰⁵(106-digit number)

16297151831399925594…20568641244005009279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.629 × 10¹⁰⁵(106-digit number)

16297151831399925594…20568641244005009281

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

3.259 × 10¹⁰⁵(106-digit number)

32594303662799851188…41137282488010018559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.259 × 10¹⁰⁵(106-digit number)

32594303662799851188…41137282488010018561

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

6.518 × 10¹⁰⁵(106-digit number)

65188607325599702377…82274564976020037119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.518 × 10¹⁰⁵(106-digit number)

65188607325599702377…82274564976020037121

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

1.303 × 10¹⁰⁶(107-digit number)

13037721465119940475…64549129952040074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.303 × 10¹⁰⁶(107-digit number)

13037721465119940475…64549129952040074241

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

2.607 × 10¹⁰⁶(107-digit number)

26075442930239880950…29098259904080148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.607 × 10¹⁰⁶(107-digit number)

26075442930239880950…29098259904080148481

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 #438,522

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