Block #922,376

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:30:00 AM · Difficulty 10.9155 · 5,881,363 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed647d96867a7215545accc68180ef9f798d790f0d669049da90135a36674d8a

View on Chainz ↗

Height

#922,376

Difficulty

10.915531

Transactions

Size

115.99 KB

Version

Bits

0aea603f

Nonce

1,437,484,216

Timestamp

2/4/2015, 10:30:00 AM

Confirmations

5,881,363

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b672d7f4906f1c5ad18e0471d4e3d0ed988cbcf7fcb9fac51718d412ec941adc

Transactions (5)

Coinbase1952f0c4596f4b…db35ca19805086

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

84dc1cb519de77…1e4dca985f8707

200 in → 1 out1005.4469 XPM28.93 KB

AKuP4XsJ…owbodNxQ

4363514325b2e0…981dae31a015ca

200 in → 1 out909.8454 XPM28.95 KB

AKuP4XsJ…owbodNxQ

80b810211d8e46…ef37b4cf20141d

200 in → 1 out997.2822 XPM28.95 KB

AKuP4XsJ…owbodNxQ

b83c0edf5ef7aa…0f6ca06209c68f

200 in → 1 out984.5013 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.

1.344 × 10⁹⁸(99-digit number)

13445428108898514719…57238893104321925119

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

1.344 × 10⁹⁸(99-digit number)

13445428108898514719…57238893104321925119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.344 × 10⁹⁸(99-digit number)

13445428108898514719…57238893104321925121

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

2.689 × 10⁹⁸(99-digit number)

26890856217797029439…14477786208643850239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.689 × 10⁹⁸(99-digit number)

26890856217797029439…14477786208643850241

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

5.378 × 10⁹⁸(99-digit number)

53781712435594058879…28955572417287700479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.378 × 10⁹⁸(99-digit number)

53781712435594058879…28955572417287700481

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

1.075 × 10⁹⁹(100-digit number)

10756342487118811775…57911144834575400959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.075 × 10⁹⁹(100-digit number)

10756342487118811775…57911144834575400961

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

2.151 × 10⁹⁹(100-digit number)

21512684974237623551…15822289669150801919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.151 × 10⁹⁹(100-digit number)

21512684974237623551…15822289669150801921

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