Block #1,411,815

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2016, 4:08:11 PM · Difficulty 10.8050 · 5,426,848 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ab66bfb1b96ad8303836b232147d45c1c15a6c62a26dfcc482b9f6488be85e3

View on Chainz ↗

Height

#1,411,815

Difficulty

10.805001

Transactions

Size

971 B

Version

Bits

0ace1485

Nonce

202,269,371

Timestamp

1/13/2016, 4:08:11 PM

Confirmations

5,426,848

Mined by

⛏️ P2SHAcijJF55Ewyzv3fjQuWfbWCTv1TA1PZE1S

Merkle Root

bed10590edbda48ef9f7b96da83f8dd7e8bae666d74425b76f94195fc28c71c9

Transactions (2)

Coinbase41c16829732bb7…7b487e2966d7de

1 in → 1 out8.5600 XPM110 B

AcijJF55…TA1PZE1S

6bb67ed40d4060…b3aa04ffa04b21

1 in → 18 out28.2367 XPM770 B

AZHRhjg9…scMau2cC AV5gWt6L…FZWcoxdh ASFJjukH…9N12FNyE AeZ2Armp…M5R78S3T ATPJ4yMa…oUsunS3P

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.

5.403 × 10⁹⁶(97-digit number)

54033333870969274800…83175740567023063039

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

5.403 × 10⁹⁶(97-digit number)

54033333870969274800…83175740567023063039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.403 × 10⁹⁶(97-digit number)

54033333870969274800…83175740567023063041

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

1.080 × 10⁹⁷(98-digit number)

10806666774193854960…66351481134046126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.080 × 10⁹⁷(98-digit number)

10806666774193854960…66351481134046126081

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

2.161 × 10⁹⁷(98-digit number)

21613333548387709920…32702962268092252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.161 × 10⁹⁷(98-digit number)

21613333548387709920…32702962268092252161

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

4.322 × 10⁹⁷(98-digit number)

43226667096775419840…65405924536184504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.322 × 10⁹⁷(98-digit number)

43226667096775419840…65405924536184504321

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

8.645 × 10⁹⁷(98-digit number)

86453334193550839680…30811849072369008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.645 × 10⁹⁷(98-digit number)

86453334193550839680…30811849072369008641

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 #1,411,815

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