Block #2,014,241

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2017, 7:21:12 PM · Difficulty 10.7022 · 4,824,980 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b28a8cc7a395b54c65a40bc2d160682e6a409f254fb18b490f08342e6a68eaf0

View on Chainz ↗

Height

#2,014,241

Difficulty

10.702234

Transactions

Size

1.72 KB

Version

Bits

0ab3c5a3

Nonce

507,958,234

Timestamp

3/8/2017, 7:21:12 PM

Confirmations

4,824,980

Mined by

⛏️ P2SHAMD6QrNYKV5D3ZJx7Jz1s7mNEqExK7r1dk

Merkle Root

75ccb71de0440d711cb27c2fd6282a261eee92c2d449694001b0fcb4bc4020a7

Transactions (2)

Coinbase20f29219c8fef5…cfdd01836d7a80

1 in → 1 out8.7400 XPM109 B

AMD6QrNY…ExK7r1dk

8274c9d96aa70e…48b506406c17de

10 in → 2 out2.2423 XPM1.52 KB

AXj5ukhd…pjoM1aHU ARumwLFi…2y4qaVeM

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.

7.566 × 10⁹⁴(95-digit number)

75667115706495761128…21328371627708966879

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

7.566 × 10⁹⁴(95-digit number)

75667115706495761128…21328371627708966879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.566 × 10⁹⁴(95-digit number)

75667115706495761128…21328371627708966881

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

1.513 × 10⁹⁵(96-digit number)

15133423141299152225…42656743255417933759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.513 × 10⁹⁵(96-digit number)

15133423141299152225…42656743255417933761

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

3.026 × 10⁹⁵(96-digit number)

30266846282598304451…85313486510835867519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.026 × 10⁹⁵(96-digit number)

30266846282598304451…85313486510835867521

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

6.053 × 10⁹⁵(96-digit number)

60533692565196608903…70626973021671735039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.053 × 10⁹⁵(96-digit number)

60533692565196608903…70626973021671735041

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

1.210 × 10⁹⁶(97-digit number)

12106738513039321780…41253946043343470079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.210 × 10⁹⁶(97-digit number)

12106738513039321780…41253946043343470081

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 #2,014,241

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