Block #2,916,558

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/9/2018, 10:17:26 PM · Difficulty 11.4318 · 3,924,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c6427095467be71559259f120813aedfa5da68f29b5a7a90c64c32a0214f0b2

View on Chainz ↗

Height

#2,916,558

Difficulty

11.431818

Transactions

Size

1.49 KB

Version

Bits

0b6e8b9c

Nonce

1,117,499,651

Timestamp

11/9/2018, 10:17:26 PM

Confirmations

3,924,576

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

dfe9d6a9ada89b3e414dfd26618a674c67536a26b029f180034a42c6c6173ccb

Transactions (5)

Coinbasec2f07be98f7415…c85c9bb9d5b36e

1 in → 1 out7.6800 XPM110 B

AbXwmGxD…4XXYP765

6da8995cb4d8fd…c25c35c45529a8

2 in → 2 out15.0900 XPM306 B

APVKWthF…PMMxwRoz AQS8SRRd…uALnJ1RV

d85d4030b072e3…75daccf7e6f848

2 in → 2 out15.0900 XPM307 B

AUmvbxZB…qfZBdnQz ASYezxNd…uerEgrAq

ad04c13e0f76ed…54e1b5ebd8535b

2 in → 2 out10.2000 XPM340 B

AZoByMEn…tvhgJCw9 AM6XD26m…RcphfPC1

13a3d37c4c49bc…f52c98b93db9ac

2 in → 2 out10.1700 XPM374 B

AY9Ezvt6…CN1iVeYi AZW9Zv5x…mVPYfgfr

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.

9.331 × 10⁹⁷(98-digit number)

93317848218785081668…05579978671694479359

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

9.331 × 10⁹⁷(98-digit number)

93317848218785081668…05579978671694479359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.331 × 10⁹⁷(98-digit number)

93317848218785081668…05579978671694479361

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

1.866 × 10⁹⁸(99-digit number)

18663569643757016333…11159957343388958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.866 × 10⁹⁸(99-digit number)

18663569643757016333…11159957343388958721

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

3.732 × 10⁹⁸(99-digit number)

37327139287514032667…22319914686777917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.732 × 10⁹⁸(99-digit number)

37327139287514032667…22319914686777917441

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

7.465 × 10⁹⁸(99-digit number)

74654278575028065334…44639829373555834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.465 × 10⁹⁸(99-digit number)

74654278575028065334…44639829373555834881

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

1.493 × 10⁹⁹(100-digit number)

14930855715005613066…89279658747111669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.493 × 10⁹⁹(100-digit number)

14930855715005613066…89279658747111669761

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

2.986 × 10⁹⁹(100-digit number)

29861711430011226133…78559317494223339519

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 #2,916,558

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