Block #376,101

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 4:36:13 AM · Difficulty 10.4228 · 6,438,775 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec2fe5d94d558963a438cad8cf78c41b95f7cd1a022ace2ca05212544141970e

View on Chainz ↗

Height

#376,101

Difficulty

10.422810

Transactions

Size

1.04 KB

Version

Bits

0a6c3d3f

Nonce

224,752

Timestamp

1/26/2014, 4:36:13 AM

Confirmations

6,438,775

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0db183e2a9fb81dc7826083a147335618a51ef291e181a2ca64dee2a9f97065d

Transactions (3)

Coinbase5eaa92c0f55d56…9c8c4e33a3492f

1 in → 1 out9.2146 XPM110 B

AeKNrjNj…1NEq95Ta

d995f0945ff308…ef52a1aa9e7dc5

3 in → 1 out1.4000 XPM488 B

AS7P17b9…dno5pdsY

d4cfb3e2c3398d…dcd679329e3977

2 in → 2 out1.1692 XPM374 B

AcvAg1zw…shKmC5J3 ANwsuoHu…Bo5hNrci

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.

2.204 × 10⁹³(94-digit number)

22045831078253849723…72935363100389401749

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

2.204 × 10⁹³(94-digit number)

22045831078253849723…72935363100389401749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.204 × 10⁹³(94-digit number)

22045831078253849723…72935363100389401751

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

4.409 × 10⁹³(94-digit number)

44091662156507699447…45870726200778803499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.409 × 10⁹³(94-digit number)

44091662156507699447…45870726200778803501

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

8.818 × 10⁹³(94-digit number)

88183324313015398894…91741452401557606999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.818 × 10⁹³(94-digit number)

88183324313015398894…91741452401557607001

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

1.763 × 10⁹⁴(95-digit number)

17636664862603079778…83482904803115213999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.763 × 10⁹⁴(95-digit number)

17636664862603079778…83482904803115214001

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

3.527 × 10⁹⁴(95-digit number)

35273329725206159557…66965809606230427999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.527 × 10⁹⁴(95-digit number)

35273329725206159557…66965809606230428001

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 #376,101

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