Block #922,278

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:34:50 AM · Difficulty 10.9158 · 5,888,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad23f88bda531f4bda17fbf17f15c003fa42691e4bc4455cbe408edf260c13da

View on Chainz ↗

Height

#922,278

Difficulty

10.915813

Transactions

Size

115.97 KB

Version

Bits

0aea72b2

Nonce

250,320,384

Timestamp

2/4/2015, 8:34:50 AM

Confirmations

5,888,859

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fd1bf1a4cb86269cb76c7fdbd7c5fba6be37bcf3e6fc86f6f73a9a2b34a55490

Transactions (5)

Coinbase36d34b7e4701f1…48c14cb157b318

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

2f5f5f52bc068d…66bdbf58489749

200 in → 1 out1046.3688 XPM28.96 KB

AKuP4XsJ…owbodNxQ

e3aab2c8b23315…8bd5d98792c79a

200 in → 1 out1028.8703 XPM28.93 KB

AKuP4XsJ…owbodNxQ

3f178c19084033…c515f2ee1f80ab

200 in → 1 out980.5888 XPM28.94 KB

AKuP4XsJ…owbodNxQ

8567e2be01df26…1bec7a6322b6e2

200 in → 1 out1067.6299 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.

1.738 × 10⁹⁵(96-digit number)

17383615497400502655…66097424385370410779

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

1.738 × 10⁹⁵(96-digit number)

17383615497400502655…66097424385370410779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.738 × 10⁹⁵(96-digit number)

17383615497400502655…66097424385370410781

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

3.476 × 10⁹⁵(96-digit number)

34767230994801005310…32194848770740821559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.476 × 10⁹⁵(96-digit number)

34767230994801005310…32194848770740821561

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

6.953 × 10⁹⁵(96-digit number)

69534461989602010620…64389697541481643119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.953 × 10⁹⁵(96-digit number)

69534461989602010620…64389697541481643121

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

1.390 × 10⁹⁶(97-digit number)

13906892397920402124…28779395082963286239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.390 × 10⁹⁶(97-digit number)

13906892397920402124…28779395082963286241

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

2.781 × 10⁹⁶(97-digit number)

27813784795840804248…57558790165926572479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.781 × 10⁹⁶(97-digit number)

27813784795840804248…57558790165926572481

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 #922,278

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