Block #922,421

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 11:22:46 AM · Difficulty 10.9154 · 5,882,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44223feeb59cb0e8f9035274215e6744b8e842d7afcead477c9fd13bb0c9467b

View on Chainz ↗

Height

#922,421

Difficulty

10.915427

Transactions

Size

116.00 KB

Version

Bits

0aea5971

Nonce

663,255,303

Timestamp

2/4/2015, 11:22:46 AM

Confirmations

5,882,779

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e3ea86051969ee99870d821726f0ad23b8db8bd992921295e4dc90b88a75ec7f

Transactions (5)

Coinbased0d978f68e166a…ecf2f4d3595f8e

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

a1e1339d123f64…c64861a0c2aea1

200 in → 1 out1155.4207 XPM28.96 KB

AKuP4XsJ…owbodNxQ

a22d398bcf83f0…94229ac8845faf

200 in → 1 out822.1975 XPM28.95 KB

AKuP4XsJ…owbodNxQ

3c354e9cbe88f9…525c13e8f281c2

200 in → 1 out1012.4254 XPM28.95 KB

AKuP4XsJ…owbodNxQ

111597c31be1a5…0ecaba9c3d60ec

200 in → 1 out980.9402 XPM28.95 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.

3.533 × 10⁹⁸(99-digit number)

35338427800711400741…01499072741701959679

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

3.533 × 10⁹⁸(99-digit number)

35338427800711400741…01499072741701959679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.533 × 10⁹⁸(99-digit number)

35338427800711400741…01499072741701959681

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

7.067 × 10⁹⁸(99-digit number)

70676855601422801483…02998145483403919359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.067 × 10⁹⁸(99-digit number)

70676855601422801483…02998145483403919361

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

1.413 × 10⁹⁹(100-digit number)

14135371120284560296…05996290966807838719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.413 × 10⁹⁹(100-digit number)

14135371120284560296…05996290966807838721

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

2.827 × 10⁹⁹(100-digit number)

28270742240569120593…11992581933615677439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.827 × 10⁹⁹(100-digit number)

28270742240569120593…11992581933615677441

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

5.654 × 10⁹⁹(100-digit number)

56541484481138241186…23985163867231354879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.654 × 10⁹⁹(100-digit number)

56541484481138241186…23985163867231354881

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