Block #2,699,354

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/10/2018, 8:57:07 AM · Difficulty 11.6444 · 4,141,587 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e500e8073f6404625e27c3ac907ef73ad9a1f79f6ae826f82f36ff982d73a02

View on Chainz ↗

Height

#2,699,354

Difficulty

11.644370

Transactions

Size

1.08 KB

Version

Bits

0ba4f577

Nonce

455,818,785

Timestamp

6/10/2018, 8:57:07 AM

Confirmations

4,141,587

Mined by

⛏️ P2SHANdXHg9TRjwUv8Lz6DzpSpaDD5kL4NtBKs

Merkle Root

56aea5f5fe553e2327e60c46495bd8229fb6efe2e7f63555a62f75e004ef5559

Transactions (5)

Coinbase3b572b4567d10a…21da5c5e879337

1 in → 1 out7.4000 XPM110 B

ANdXHg9T…kL4NtBKs

fa4b4354538b91…e969fdd7beb322

1 in → 2 out498.9762 XPM226 B

AVmWcN4r…HxmgEJjN AGzrd4MM…7HC9qVLn

9c817f495a10f4…162eb35b3881f9

1 in → 2 out375.5459 XPM226 B

ASxSxE3B…7okn2Ng6 AdZ6QpK5…4sC1SzsM

d63ace91df84e0…45fef03081a172

1 in → 2 out154.8590 XPM225 B

ARowkdQF…9LydsRKD AGpNcnjX…ExiscN2C

f62a7921420d68…d28272d1be5b4a

1 in → 2 out149.7745 XPM226 B

ASk1JkYA…EmKWfKkB AMvkTFJq…uuuidGHd

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.

9.992 × 10⁹⁶(97-digit number)

99925653513791212874…12563641042509246719

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

9.992 × 10⁹⁶(97-digit number)

99925653513791212874…12563641042509246719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.992 × 10⁹⁶(97-digit number)

99925653513791212874…12563641042509246721

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

1.998 × 10⁹⁷(98-digit number)

19985130702758242574…25127282085018493439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.998 × 10⁹⁷(98-digit number)

19985130702758242574…25127282085018493441

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

3.997 × 10⁹⁷(98-digit number)

39970261405516485149…50254564170036986879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.997 × 10⁹⁷(98-digit number)

39970261405516485149…50254564170036986881

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

7.994 × 10⁹⁷(98-digit number)

79940522811032970299…00509128340073973759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.994 × 10⁹⁷(98-digit number)

79940522811032970299…00509128340073973761

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

1.598 × 10⁹⁸(99-digit number)

15988104562206594059…01018256680147947519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.598 × 10⁹⁸(99-digit number)

15988104562206594059…01018256680147947521

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

3.197 × 10⁹⁸(99-digit number)

31976209124413188119…02036513360295895039

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 #2,699,354

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