Block #2,789,411

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/11/2018, 3:52:18 PM · Difficulty 11.6719 · 4,015,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46081bd6f0d50ecdf515239daf35ab9c889b8fd194acb122336bc85f77c18735

View on Chainz ↗

Height

#2,789,411

Difficulty

11.671914

Transactions

Size

846 B

Version

Bits

0bac028a

Nonce

1,302,807,134

Timestamp

8/11/2018, 3:52:18 PM

Confirmations

4,015,632

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

f9a3680a1166fdf31155533d184e1c6f897cac34b679af551632508993b2cd15

Transactions (3)

Coinbase786ea4f7241f73…e5fdf4c3a0f881

1 in → 1 out7.3500 XPM110 B

AZtxQr2F…7grUWrUz

212a2b9e6bb6ef…f3492bf51879ae

2 in → 2 out14.8000 XPM306 B

Ademh2BR…aaAJ12fp AKD9LeNP…bQTn8mEf

c21e9fcca86902…0aa9e153c9b7cd

2 in → 2 out12.3800 XPM339 B

AbtKavfP…J9MGe51b AKShREuq…PyYH5DXw

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.

1.291 × 10⁹⁶(97-digit number)

12911209788511814361…85481069162558572799

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

1.291 × 10⁹⁶(97-digit number)

12911209788511814361…85481069162558572799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.291 × 10⁹⁶(97-digit number)

12911209788511814361…85481069162558572801

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

2.582 × 10⁹⁶(97-digit number)

25822419577023628722…70962138325117145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.582 × 10⁹⁶(97-digit number)

25822419577023628722…70962138325117145601

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

5.164 × 10⁹⁶(97-digit number)

51644839154047257445…41924276650234291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.164 × 10⁹⁶(97-digit number)

51644839154047257445…41924276650234291201

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

1.032 × 10⁹⁷(98-digit number)

10328967830809451489…83848553300468582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.032 × 10⁹⁷(98-digit number)

10328967830809451489…83848553300468582401

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

2.065 × 10⁹⁷(98-digit number)

20657935661618902978…67697106600937164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.065 × 10⁹⁷(98-digit number)

20657935661618902978…67697106600937164801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.131 × 10⁹⁷(98-digit number)

41315871323237805956…35394213201874329599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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