Block #922,473

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 12:24:14 PM · Difficulty 10.9152 · 5,872,684 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d3818d3fdc4da2913b3af86cee828a82cdd9bf998ef5b7f1d5c61ab68bde65c

View on Chainz ↗

Height

#922,473

Difficulty

10.915249

Transactions

Size

116.04 KB

Version

Bits

0aea4dbb

Nonce

897,279,594

Timestamp

2/4/2015, 12:24:14 PM

Confirmations

5,872,684

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

829d3426bf30205a7e528d271fe1122c5ad49a4765ed3ca1999a8d87b645b2e0

Transactions (5)

Coinbase2be379f31c6c0b…c1c1d5fdf19e68

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

fadad9ab6f733b…29bcc1a1dce209

200 in → 1 out1048.9470 XPM28.96 KB

AKuP4XsJ…owbodNxQ

def1e4979bd926…bfabef723f1c7b

200 in → 1 out901.2988 XPM28.96 KB

AKuP4XsJ…owbodNxQ

c20ab8791f2d78…4ac917a8ed54fb

200 in → 1 out889.6559 XPM28.96 KB

AKuP4XsJ…owbodNxQ

1e0720fcc466bf…7317d16d68087d

200 in → 1 out839.5925 XPM28.96 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.

2.365 × 10⁹⁸(99-digit number)

23652115356307004962…98298926940081356799

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

2.365 × 10⁹⁸(99-digit number)

23652115356307004962…98298926940081356799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.365 × 10⁹⁸(99-digit number)

23652115356307004962…98298926940081356801

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

4.730 × 10⁹⁸(99-digit number)

47304230712614009924…96597853880162713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.730 × 10⁹⁸(99-digit number)

47304230712614009924…96597853880162713601

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

9.460 × 10⁹⁸(99-digit number)

94608461425228019849…93195707760325427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.460 × 10⁹⁸(99-digit number)

94608461425228019849…93195707760325427201

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

1.892 × 10⁹⁹(100-digit number)

18921692285045603969…86391415520650854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.892 × 10⁹⁹(100-digit number)

18921692285045603969…86391415520650854401

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

3.784 × 10⁹⁹(100-digit number)

37843384570091207939…72782831041301708799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.784 × 10⁹⁹(100-digit number)

37843384570091207939…72782831041301708801

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