Block #338,346

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2014, 9:19:39 AM · Difficulty 10.1195 · 6,470,733 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41a46984b5bd6a25b9dda42bbd2936f58c42160f5e4b26663e60c2f5d01cbefa

View on Chainz ↗

Height

#338,346

Difficulty

10.119548

Transactions

Size

1.08 KB

Version

Bits

0a1e9ab4

Nonce

5,629

Timestamp

1/1/2014, 9:19:39 AM

Confirmations

6,470,733

Mined by

⛏️ aR2Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

8d842c8d218ac7e7733f18973cecac8b1b462869719e76f6be4d6238f22462c2

Transactions (1)

Coinbase8d842c8d218ac7…4d6238f22462c2

1 in → 28 out9.7300 XPM1015 B

Aac9Hjdg…P4ktypc3 AUe9Js7F…AxUTquTa AFpbuSgY…J2xyG5Rg AQ8QAT3J…rCFKuVbR APeshfYV…3PKcKMKH

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.

6.626 × 10⁹⁴(95-digit number)

66267667028356791192…28184487706650410239

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

6.626 × 10⁹⁴(95-digit number)

66267667028356791192…28184487706650410239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.626 × 10⁹⁴(95-digit number)

66267667028356791192…28184487706650410241

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

1.325 × 10⁹⁵(96-digit number)

13253533405671358238…56368975413300820479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.325 × 10⁹⁵(96-digit number)

13253533405671358238…56368975413300820481

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

2.650 × 10⁹⁵(96-digit number)

26507066811342716477…12737950826601640959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.650 × 10⁹⁵(96-digit number)

26507066811342716477…12737950826601640961

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

5.301 × 10⁹⁵(96-digit number)

53014133622685432954…25475901653203281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.301 × 10⁹⁵(96-digit number)

53014133622685432954…25475901653203281921

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

1.060 × 10⁹⁶(97-digit number)

10602826724537086590…50951803306406563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.060 × 10⁹⁶(97-digit number)

10602826724537086590…50951803306406563841

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 #338,346

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