Block #381,442

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 12:11:18 AM · Difficulty 10.4060 · 6,433,029 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4723468b336680264c0c92f6d901f4601a03c31f5935fd2b5777acaf8779650d

View on Chainz ↗

Height

#381,442

Difficulty

10.405999

Transactions

Size

1.23 KB

Version

Bits

0a67ef8f

Nonce

90,425

Timestamp

1/30/2014, 12:11:18 AM

Confirmations

6,433,029

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d33732ccf3a36ac47ab6c9238c818b89f91bd50bfb21003b01fd043bad168308

Transactions (5)

Coinbase1d4db74c822ed4…8d56773aa9a5b8

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

4ed49e1f01593f…1d10854ad5a3de

1 in → 2 out6.1023 XPM226 B

ARpzqnUm…DmQAk68w ASsLhegi…XREhwbJB

d0f753171ef717…2f26769b21629d

1 in → 2 out2.1430 XPM226 B

AKJZGvLQ…Qn9KzMD1 ARyiJjKt…g4bmJD4o

5845fc67a4e934…635ab92f1e417e

1 in → 2 out3.1569 XPM227 B

AMHXhYwZ…ZU3VPLem AewB4Mzt…FE12Dfxu

80106974c6762e…1cabf3619bbbca

2 in → 2 out1.0369 XPM373 B

ATEhhiKB…RxD17TvE AHK1An2Q…sepRq4Z6

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.

4.148 × 10⁹¹(92-digit number)

41487070921260904479…27413532599099972839

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

4.148 × 10⁹¹(92-digit number)

41487070921260904479…27413532599099972839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.148 × 10⁹¹(92-digit number)

41487070921260904479…27413532599099972841

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

8.297 × 10⁹¹(92-digit number)

82974141842521808958…54827065198199945679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.297 × 10⁹¹(92-digit number)

82974141842521808958…54827065198199945681

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

1.659 × 10⁹²(93-digit number)

16594828368504361791…09654130396399891359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.659 × 10⁹²(93-digit number)

16594828368504361791…09654130396399891361

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

3.318 × 10⁹²(93-digit number)

33189656737008723583…19308260792799782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.318 × 10⁹²(93-digit number)

33189656737008723583…19308260792799782721

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

6.637 × 10⁹²(93-digit number)

66379313474017447166…38616521585599565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.637 × 10⁹²(93-digit number)

66379313474017447166…38616521585599565441

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 #381,442

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