Block #383,322

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 8:30:59 AM · Difficulty 10.3996 · 6,422,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9d527d4adf5f0b54672dfa43a6065403002d90088e97fccdf1f703950d62e95

View on Chainz ↗

Height

#383,322

Difficulty

10.399590

Transactions

Size

1.45 KB

Version

Bits

0a664b81

Nonce

50,332,400

Timestamp

1/31/2014, 8:30:59 AM

Confirmations

6,422,652

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

caba08717397ef07928968a6842bd83a12e444411e307462c656bd98bee90891

Transactions (4)

Coinbase49f7c9e2d81217…9d0f5f2218c3a9

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

2b09b30a3fb0c1…c39f78adcf01ae

2 in → 2 out85.2559 XPM375 B

ARatGy9s…p5Jd2ruG AQYbSNRU…WxLCPW5A

6d8ea805820bc1…dbb410e48e336b

2 in → 2 out8.8046 XPM375 B

ANdonQLb…3SovhKN4 AH5uzUno…CGfsa3Te

77ea99a1ddfd0f…caa2344a89974b

3 in → 2 out0.8322 XPM524 B

ANA654SS…XXR89mDn AFojiEGQ…Jz8AX8xz

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.

8.529 × 10¹⁰¹(102-digit number)

85294512300271720980…59119647887550054399

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

8.529 × 10¹⁰¹(102-digit number)

85294512300271720980…59119647887550054399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.529 × 10¹⁰¹(102-digit number)

85294512300271720980…59119647887550054401

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

1.705 × 10¹⁰²(103-digit number)

17058902460054344196…18239295775100108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.705 × 10¹⁰²(103-digit number)

17058902460054344196…18239295775100108801

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

3.411 × 10¹⁰²(103-digit number)

34117804920108688392…36478591550200217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.411 × 10¹⁰²(103-digit number)

34117804920108688392…36478591550200217601

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

6.823 × 10¹⁰²(103-digit number)

68235609840217376784…72957183100400435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.823 × 10¹⁰²(103-digit number)

68235609840217376784…72957183100400435201

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

1.364 × 10¹⁰³(104-digit number)

13647121968043475356…45914366200800870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.364 × 10¹⁰³(104-digit number)

13647121968043475356…45914366200800870401

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