Block #922,342

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:52:02 AM · Difficulty 10.9156 · 5,881,972 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3e6332eb49f03fbb44d92aa838d8ca2b2071243ab209a89e9fc4f2567a5afbe

View on Chainz ↗

Height

#922,342

Difficulty

10.915592

Transactions

Size

116.01 KB

Version

Bits

0aea643c

Nonce

1,525,146,117

Timestamp

2/4/2015, 9:52:02 AM

Confirmations

5,881,972

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f3ff291ac99056cc7d786720d0895eeb8cd703bf4f4011c3548f9e9aecb8fd86

Transactions (5)

Coinbase7cff56c293668f…853c6ac571904f

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

4b7bd53c2a01c7…6b99f7a25ed09a

200 in → 1 out1108.0831 XPM28.96 KB

AKuP4XsJ…owbodNxQ

f5ea68c12344b3…ea0274bc812a2b

200 in → 1 out1057.2832 XPM28.95 KB

AKuP4XsJ…owbodNxQ

1b7c35c35f65e9…f4108a33871722

200 in → 1 out1044.0856 XPM28.95 KB

AKuP4XsJ…owbodNxQ

449c354b766367…7ee333df92999a

200 in → 1 out1043.8461 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.

3.569 × 10⁹⁶(97-digit number)

35697600089973379437…53777826158481926719

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

3.569 × 10⁹⁶(97-digit number)

35697600089973379437…53777826158481926719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.569 × 10⁹⁶(97-digit number)

35697600089973379437…53777826158481926721

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

7.139 × 10⁹⁶(97-digit number)

71395200179946758875…07555652316963853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.139 × 10⁹⁶(97-digit number)

71395200179946758875…07555652316963853441

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

1.427 × 10⁹⁷(98-digit number)

14279040035989351775…15111304633927706879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.427 × 10⁹⁷(98-digit number)

14279040035989351775…15111304633927706881

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

2.855 × 10⁹⁷(98-digit number)

28558080071978703550…30222609267855413759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.855 × 10⁹⁷(98-digit number)

28558080071978703550…30222609267855413761

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

5.711 × 10⁹⁷(98-digit number)

57116160143957407100…60445218535710827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.711 × 10⁹⁷(98-digit number)

57116160143957407100…60445218535710827521

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