Block #922,281

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:39:12 AM · Difficulty 10.9158 · 5,882,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

027f2662eaebc27859cf8891fcd13c4ba888dd38245f091d32b28bc957581aed

View on Chainz ↗

Height

#922,281

Difficulty

10.915813

Transactions

Size

115.94 KB

Version

Bits

0aea72bd

Nonce

414,699,426

Timestamp

2/4/2015, 8:39:12 AM

Confirmations

5,882,834

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

27cd156487b8cb661bfb3611c26d3ea183370779003e7269bf77d47c9970c184

Transactions (5)

Coinbase3335d09594bb95…c9310642e889cf

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

425a8f72b56b53…8ff6d02cd6341d

200 in → 1 out1164.3930 XPM28.94 KB

AKuP4XsJ…owbodNxQ

b14495c4079b76…db218044acbc56

200 in → 1 out965.3556 XPM28.93 KB

AKuP4XsJ…owbodNxQ

601347cc8a49e2…46e041afa38304

200 in → 1 out1057.2475 XPM28.93 KB

AKuP4XsJ…owbodNxQ

e2d6429bae024d…a5c93c1cbe3127

200 in → 1 out929.7143 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.

1.882 × 10⁹⁴(95-digit number)

18824470993540185094…26674335469168245599

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

1.882 × 10⁹⁴(95-digit number)

18824470993540185094…26674335469168245599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.882 × 10⁹⁴(95-digit number)

18824470993540185094…26674335469168245601

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

3.764 × 10⁹⁴(95-digit number)

37648941987080370188…53348670938336491199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.764 × 10⁹⁴(95-digit number)

37648941987080370188…53348670938336491201

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

7.529 × 10⁹⁴(95-digit number)

75297883974160740377…06697341876672982399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.529 × 10⁹⁴(95-digit number)

75297883974160740377…06697341876672982401

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

1.505 × 10⁹⁵(96-digit number)

15059576794832148075…13394683753345964799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.505 × 10⁹⁵(96-digit number)

15059576794832148075…13394683753345964801

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

3.011 × 10⁹⁵(96-digit number)

30119153589664296151…26789367506691929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.011 × 10⁹⁵(96-digit number)

30119153589664296151…26789367506691929601

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