Block #2,292,818

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/12/2017, 1:44:38 AM · Difficulty 10.9548 · 4,552,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a28b828faea3a47ef40687b471dec1f42d82272ced6edd446b7b576e0face8c6

View on Chainz ↗

Height

#2,292,818

Difficulty

10.954750

Transactions

Size

1.08 KB

Version

Bits

0af46a86

Nonce

1,044,034,706

Timestamp

9/12/2017, 1:44:38 AM

Confirmations

4,552,439

Mined by

⛏️ P2SHAJn2iesdUVXFxcjaHq6y6EKcYrhQz53EuD

Merkle Root

12a6b1eb466d2741fe8e44ae9a8de55c3af515d03cff33b5f39eea2d9cb4cf74

Transactions (5)

Coinbase12486a657362a0…1579ef405a38ce

1 in → 1 out8.3600 XPM110 B

AJn2iesd…hQz53EuD

08500634737614…8cb74f6f90b35e

1 in → 2 out2969.9900 XPM225 B

ALTVqHXd…xFhEdJNC ARaNCeSx…b8M3uhxY

3a36c0ae5550e9…92b4819d28d29e

1 in → 2 out9775.8082 XPM225 B

AcYgVaPH…kLLghHxf AYjaivKf…1HHdiRbZ

38e121532e34ba…68986c32be3583

1 in → 2 out9285.5750 XPM226 B

AXgzo7Nw…Gqke5mXY ARDXuE18…fkPFqAk5

f41a737ac529fa…630c39d6d1120d

1 in → 2 out1798.8567 XPM226 B

AGYMqTYU…Wr3NDL7N AcHkHF5m…L2dB2UA5

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.

3.448 × 10⁹⁴(95-digit number)

34483851301505060619…57205823773329033599

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

3.448 × 10⁹⁴(95-digit number)

34483851301505060619…57205823773329033599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.448 × 10⁹⁴(95-digit number)

34483851301505060619…57205823773329033601

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

6.896 × 10⁹⁴(95-digit number)

68967702603010121238…14411647546658067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.896 × 10⁹⁴(95-digit number)

68967702603010121238…14411647546658067201

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

1.379 × 10⁹⁵(96-digit number)

13793540520602024247…28823295093316134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.379 × 10⁹⁵(96-digit number)

13793540520602024247…28823295093316134401

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

2.758 × 10⁹⁵(96-digit number)

27587081041204048495…57646590186632268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.758 × 10⁹⁵(96-digit number)

27587081041204048495…57646590186632268801

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

5.517 × 10⁹⁵(96-digit number)

55174162082408096990…15293180373264537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.517 × 10⁹⁵(96-digit number)

55174162082408096990…15293180373264537601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.103 × 10⁹⁶(97-digit number)

11034832416481619398…30586360746529075199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,292,818

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