Block #922,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:29:07 AM · Difficulty 10.9158 · 5,873,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bfa3423fff36c5d1f41634260702a022c7aae8c68be0a630c93b7345235672ea

View on Chainz ↗

Height

#922,274

Difficulty

10.915846

Transactions

Size

115.98 KB

Version

Bits

0aea74e9

Nonce

172,633,965

Timestamp

2/4/2015, 8:29:07 AM

Confirmations

5,873,721

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cf2e53ed97fa1d676e9b6fbaef96e2a4a8dca647c800da044b03839436330e95

Transactions (5)

Coinbase936e3990e9dcad…10707492f3f9f3

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

c00da4f7d49ed8…a83d2e98c32ba0

200 in → 1 out1102.6432 XPM28.95 KB

AKuP4XsJ…owbodNxQ

0374cc89e1d019…958cda289236ef

200 in → 1 out898.4508 XPM28.94 KB

AKuP4XsJ…owbodNxQ

b0d48f4bf4fd4f…2ee96c3c1b169f

200 in → 1 out1053.5182 XPM28.95 KB

AKuP4XsJ…owbodNxQ

20d7deb6401650…9b82fc28ef02bb

200 in → 1 out1098.9195 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.

8.596 × 10⁹⁵(96-digit number)

85967043268166428762…86285565422964365439

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

8.596 × 10⁹⁵(96-digit number)

85967043268166428762…86285565422964365439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.596 × 10⁹⁵(96-digit number)

85967043268166428762…86285565422964365441

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

1.719 × 10⁹⁶(97-digit number)

17193408653633285752…72571130845928730879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.719 × 10⁹⁶(97-digit number)

17193408653633285752…72571130845928730881

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

3.438 × 10⁹⁶(97-digit number)

34386817307266571505…45142261691857461759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.438 × 10⁹⁶(97-digit number)

34386817307266571505…45142261691857461761

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

6.877 × 10⁹⁶(97-digit number)

68773634614533143010…90284523383714923519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.877 × 10⁹⁶(97-digit number)

68773634614533143010…90284523383714923521

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

1.375 × 10⁹⁷(98-digit number)

13754726922906628602…80569046767429847039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.375 × 10⁹⁷(98-digit number)

13754726922906628602…80569046767429847041

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