Block #341,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 9:23:59 AM · Difficulty 10.1358 · 6,476,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

adaec622e672f6e0323775f85ec8e5e15f661e0159e71f89d16b474ddca84a8e

View on Chainz ↗

Height

#341,320

Difficulty

10.135752

Transactions

Size

1.41 KB

Version

Bits

0a22c0a8

Nonce

25,974

Timestamp

1/3/2014, 9:23:59 AM

Confirmations

6,476,621

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a56d75bbd13184e77900df382575a916a55dc2bc175c1b9d372c38fc94206876

Transactions (4)

Coinbase32d04d9d6d6416…c7ddc534645b55

1 in → 1 out9.7500 XPM110 B

AeKNrjNj…1NEq95Ta

f1d56b8f43b8f0…fb45350e7cc6ae

2 in → 1 out153.5900 XPM340 B

AeCHesRA…UxJNU5iR

5234ea1029e66b…8159c43651f1a2

2 in → 2 out55.5494 XPM374 B

AVzMcgGV…1dXogD7T Af6qiLPa…C9fx7Xmx

2f0b900ae61b71…284db8992b8037

3 in → 2 out19.8161 XPM523 B

ATRZcgbY…dJWs58dG AJdoVeQM…MG8mfq87

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.

3.429 × 10¹⁰³(104-digit number)

34299663105080206968…03800877253881487359

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

3.429 × 10¹⁰³(104-digit number)

34299663105080206968…03800877253881487359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.429 × 10¹⁰³(104-digit number)

34299663105080206968…03800877253881487361

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

6.859 × 10¹⁰³(104-digit number)

68599326210160413936…07601754507762974719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.859 × 10¹⁰³(104-digit number)

68599326210160413936…07601754507762974721

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

1.371 × 10¹⁰⁴(105-digit number)

13719865242032082787…15203509015525949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.371 × 10¹⁰⁴(105-digit number)

13719865242032082787…15203509015525949441

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

2.743 × 10¹⁰⁴(105-digit number)

27439730484064165574…30407018031051898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.743 × 10¹⁰⁴(105-digit number)

27439730484064165574…30407018031051898881

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

5.487 × 10¹⁰⁴(105-digit number)

54879460968128331149…60814036062103797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.487 × 10¹⁰⁴(105-digit number)

54879460968128331149…60814036062103797761

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 #341,320

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