Block #922,448

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 11:54:12 AM · Difficulty 10.9153 · 5,880,688 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65ad89f38a41eec3183dc8e16c3fb40d3543ac758a6ec2d34ae4be99651e8764

View on Chainz ↗

Height

#922,448

Difficulty

10.915322

Transactions

Size

116.03 KB

Version

Bits

0aea528b

Nonce

77,883,978

Timestamp

2/4/2015, 11:54:12 AM

Confirmations

5,880,688

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1d0584681843898fba008752c5042e98c64a57b7f07736af671b04ca09d88c3c

Transactions (5)

Coinbaseafd5706b815f09…8ee7a8af12b79d

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

df6f7525b2d92a…379632ae0b570f

200 in → 1 out1019.9753 XPM28.96 KB

AKuP4XsJ…owbodNxQ

9ac66a43bdb432…b2fe786ebb9803

200 in → 1 out978.6033 XPM28.96 KB

AKuP4XsJ…owbodNxQ

043f0c3b769f5c…0eceddb965c833

200 in → 1 out1035.6497 XPM28.96 KB

AKuP4XsJ…owbodNxQ

22af3488a8305d…a57799163ec6ee

200 in → 1 out1000.5261 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.

1.313 × 10⁹⁸(99-digit number)

13131807781539049707…18418344031567871999

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

1.313 × 10⁹⁸(99-digit number)

13131807781539049707…18418344031567871999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.313 × 10⁹⁸(99-digit number)

13131807781539049707…18418344031567872001

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

2.626 × 10⁹⁸(99-digit number)

26263615563078099415…36836688063135743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.626 × 10⁹⁸(99-digit number)

26263615563078099415…36836688063135744001

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

5.252 × 10⁹⁸(99-digit number)

52527231126156198831…73673376126271487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.252 × 10⁹⁸(99-digit number)

52527231126156198831…73673376126271488001

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

1.050 × 10⁹⁹(100-digit number)

10505446225231239766…47346752252542975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.050 × 10⁹⁹(100-digit number)

10505446225231239766…47346752252542976001

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

2.101 × 10⁹⁹(100-digit number)

21010892450462479532…94693504505085951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.101 × 10⁹⁹(100-digit number)

21010892450462479532…94693504505085952001

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