Block #922,353

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:07:43 AM · Difficulty 10.9155 · 5,872,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ce392b3b4fe95198805044288d52594c7cba35522ac4fe974e9f0fa40f99d5c

View on Chainz ↗

Height

#922,353

Difficulty

10.915531

Transactions

Size

115.94 KB

Version

Bits

0aea6040

Nonce

591,559,678

Timestamp

2/4/2015, 10:07:43 AM

Confirmations

5,872,455

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8d9997c5b775fc2e529934fcc78c2b411678122b01b3df30314fad5a7c25066c

Transactions (5)

Coinbaseef0c8b76187060…cd15ff6770aae7

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

868dc8fbd2f4d6…196012f355c327

200 in → 1 out1130.0496 XPM28.95 KB

AKuP4XsJ…owbodNxQ

9b0a9945b24b64…66d37b1555de4c

200 in → 1 out1102.8640 XPM28.92 KB

AKuP4XsJ…owbodNxQ

0c24fff84398d3…01c84eb188d0a9

200 in → 1 out960.8825 XPM28.93 KB

AKuP4XsJ…owbodNxQ

583c9734433d99…466d7dda31ccc4

200 in → 1 out856.8061 XPM28.94 KB

AKuP4XsJ…owbodNxQ

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.

1.832 × 10⁹⁶(97-digit number)

18326375101460794302…24321427452883219839

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

1.832 × 10⁹⁶(97-digit number)

18326375101460794302…24321427452883219839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.832 × 10⁹⁶(97-digit number)

18326375101460794302…24321427452883219841

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

3.665 × 10⁹⁶(97-digit number)

36652750202921588605…48642854905766439679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.665 × 10⁹⁶(97-digit number)

36652750202921588605…48642854905766439681

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

7.330 × 10⁹⁶(97-digit number)

73305500405843177210…97285709811532879359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.330 × 10⁹⁶(97-digit number)

73305500405843177210…97285709811532879361

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

1.466 × 10⁹⁷(98-digit number)

14661100081168635442…94571419623065758719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.466 × 10⁹⁷(98-digit number)

14661100081168635442…94571419623065758721

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

2.932 × 10⁹⁷(98-digit number)

29322200162337270884…89142839246131517439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.932 × 10⁹⁷(98-digit number)

29322200162337270884…89142839246131517441

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