Block #422,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 12:05:48 PM · Difficulty 10.3793 · 6,394,108 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abe844c00bfae7e117668bb9b2d87dab5be43266aef6e62ee068de16933a80d3

View on Chainz ↗

Height

#422,112

Difficulty

10.379308

Transactions

Size

651 B

Version

Bits

0a611a5a

Nonce

160,663

Timestamp

2/27/2014, 12:05:48 PM

Confirmations

6,394,108

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7a19303939de025e48b90c0462cec72bfb1650808ef92bf9cb3a6f1fad55658f

Transactions (2)

Coinbase1cd2f1557d4920…721d76667d0e53

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

4f7bdc09ba6943…8ef6f68490c20c

2 in → 6 out18.5600 XPM442 B

AT8oCE2C…inTrzTXz AQufhWCK…onJSt1Rt AazSmBdf…MMGyURcV AeKNrjNj…1NEq95Ta AXqCJxua…RZtym3F2

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.

7.724 × 10¹⁰¹(102-digit number)

77246426545834959962…47638420326438010879

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

7.724 × 10¹⁰¹(102-digit number)

77246426545834959962…47638420326438010879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.724 × 10¹⁰¹(102-digit number)

77246426545834959962…47638420326438010881

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

1.544 × 10¹⁰²(103-digit number)

15449285309166991992…95276840652876021759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.544 × 10¹⁰²(103-digit number)

15449285309166991992…95276840652876021761

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

3.089 × 10¹⁰²(103-digit number)

30898570618333983984…90553681305752043519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.089 × 10¹⁰²(103-digit number)

30898570618333983984…90553681305752043521

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

6.179 × 10¹⁰²(103-digit number)

61797141236667967969…81107362611504087039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.179 × 10¹⁰²(103-digit number)

61797141236667967969…81107362611504087041

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

1.235 × 10¹⁰³(104-digit number)

12359428247333593593…62214725223008174079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.235 × 10¹⁰³(104-digit number)

12359428247333593593…62214725223008174081

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

Block #422,112

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