Block #2,801,894

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/20/2018, 8:27:17 AM · Difficulty 11.6703 · 4,038,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68997504c9ebe4ec0dfa1c44e209c6b28278d063bdc490d89ebe4daf67fe3b61

View on Chainz ↗

Height

#2,801,894

Difficulty

11.670325

Transactions

Size

1.75 KB

Version

Bits

0bab9a6a

Nonce

1,210,399,338

Timestamp

8/20/2018, 8:27:17 AM

Confirmations

4,038,566

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

8ec136988559cbb5115cd6e39f6e95a7207d8cbd578bb2f54df640d7fc920539

Transactions (5)

Coinbase8fce7de373b7ff…934df8f41845d0

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

7f82ee433d98fd…73dc007021821d

2 in → 2 out14.6300 XPM306 B

AXxEpimC…EbMzYSLd APVKWthF…PMMxwRoz

a55ad28d9517a2…32538b5ad39a8e

2 in → 2 out12.2500 XPM340 B

AKtg5M5J…UY3VCdzE AYBqE5pt…cWGVGjDD

5bd7c42856c1e5…6d89df2bcd3d45

2 in → 2 out11.9400 XPM340 B

AcraKfkB…dkR7Yuu5 AW3QZZmg…j2rGjUkp

ab63581000937d…324d23d62e0ba1

4 in → 1 out10.0000 XPM603 B

AGoYowqV…s8a6cKpk

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.

2.355 × 10⁹⁴(95-digit number)

23556777057147056195…07218170323092493119

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

2.355 × 10⁹⁴(95-digit number)

23556777057147056195…07218170323092493119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.355 × 10⁹⁴(95-digit number)

23556777057147056195…07218170323092493121

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

4.711 × 10⁹⁴(95-digit number)

47113554114294112391…14436340646184986239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.711 × 10⁹⁴(95-digit number)

47113554114294112391…14436340646184986241

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

9.422 × 10⁹⁴(95-digit number)

94227108228588224782…28872681292369972479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.422 × 10⁹⁴(95-digit number)

94227108228588224782…28872681292369972481

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

1.884 × 10⁹⁵(96-digit number)

18845421645717644956…57745362584739944959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.884 × 10⁹⁵(96-digit number)

18845421645717644956…57745362584739944961

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

3.769 × 10⁹⁵(96-digit number)

37690843291435289913…15490725169479889919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.769 × 10⁹⁵(96-digit number)

37690843291435289913…15490725169479889921

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

7.538 × 10⁹⁵(96-digit number)

75381686582870579826…30981450338959779839

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

Block #2,801,894

Cookie Preferences