Block #350,756

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 6:48:01 AM · Difficulty 10.2867 · 6,479,704 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

877e7e5879c51d8dcbf2538d490d4383db79f0334ebe81a09186015c0c492dd7

View on Chainz ↗

Height

#350,756

Difficulty

10.286671

Transactions

Size

1.43 KB

Version

Bits

0a49634b

Nonce

66,506

Timestamp

1/9/2014, 6:48:01 AM

Confirmations

6,479,704

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

18284772f9f9a39dca66b2ab2aad06f8d7cb25667a1a14a2c37ec5cb7fe2867a

Transactions (4)

Coinbase2ad6eb3a512fd1…d790437bc11d28

1 in → 1 out9.4700 XPM110 B

AeKNrjNj…1NEq95Ta

32e6456c2ceed4…4315877de38c45

4 in → 8 out21.8742 XPM806 B

AN3r4D36…jEiyTM3F AeKNrjNj…1NEq95Ta AJQWwVXB…L2b71Qbt AeTeGX3T…2Nm2Fveq AXwoC6Y4…Bb3zMSZ2

873a9fd6008048…a9b4406ec1ab07

1 in → 2 out6.4411 XPM226 B

AGmPPjEv…LFRYhG3Y ANH2ugoT…MYH9p9NV

793b2553274ca1…a5fe236531724e

1 in → 2 out6.4665 XPM227 B

AYDt95bR…2CUsyh6K AZJMR7eK…X89fnJmR

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.

8.028 × 10⁹⁶(97-digit number)

80289578095240817478…35201321007219958019

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

8.028 × 10⁹⁶(97-digit number)

80289578095240817478…35201321007219958019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.028 × 10⁹⁶(97-digit number)

80289578095240817478…35201321007219958021

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

1.605 × 10⁹⁷(98-digit number)

16057915619048163495…70402642014439916039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.605 × 10⁹⁷(98-digit number)

16057915619048163495…70402642014439916041

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

3.211 × 10⁹⁷(98-digit number)

32115831238096326991…40805284028879832079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.211 × 10⁹⁷(98-digit number)

32115831238096326991…40805284028879832081

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

6.423 × 10⁹⁷(98-digit number)

64231662476192653983…81610568057759664159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.423 × 10⁹⁷(98-digit number)

64231662476192653983…81610568057759664161

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

1.284 × 10⁹⁸(99-digit number)

12846332495238530796…63221136115519328319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.284 × 10⁹⁸(99-digit number)

12846332495238530796…63221136115519328321

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 #350,756

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