Block #2,992,105

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/2/2019, 7:39:31 AM · Difficulty 11.2630 · 3,841,166 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

546f35c25ab67c20e90c457c2abd8856a51e023eea1e27501ffc3ff0ca1b3973

View on Chainz ↗

Height

#2,992,105

Difficulty

11.263015

Transactions

Size

1.52 KB

Version

Bits

0b4354f5

Nonce

648,198,184

Timestamp

1/2/2019, 7:39:31 AM

Confirmations

3,841,166

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

357026133ceb61565b8e13bc69696d668c5c1932dfea7bbd44e3588d0bfc74cb

Transactions (2)

Coinbaseb4280c0887e6e2…18adcc6f0a865c

1 in → 1 out7.8900 XPM110 B

AUhjokok…k5m93PZR

36d0f904856e54…8413a24a965951

10 in → 2 out50.0410 XPM1.32 KB

AJktnhjX…XNqNLjQX AbXwmGxD…4XXYP765

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.

4.519 × 10⁹⁶(97-digit number)

45193874302589904120…65471526405403750399

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

4.519 × 10⁹⁶(97-digit number)

45193874302589904120…65471526405403750399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.519 × 10⁹⁶(97-digit number)

45193874302589904120…65471526405403750401

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

9.038 × 10⁹⁶(97-digit number)

90387748605179808240…30943052810807500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.038 × 10⁹⁶(97-digit number)

90387748605179808240…30943052810807500801

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

1.807 × 10⁹⁷(98-digit number)

18077549721035961648…61886105621615001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.807 × 10⁹⁷(98-digit number)

18077549721035961648…61886105621615001601

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

3.615 × 10⁹⁷(98-digit number)

36155099442071923296…23772211243230003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.615 × 10⁹⁷(98-digit number)

36155099442071923296…23772211243230003201

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

7.231 × 10⁹⁷(98-digit number)

72310198884143846592…47544422486460006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.231 × 10⁹⁷(98-digit number)

72310198884143846592…47544422486460006401

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

1.446 × 10⁹⁸(99-digit number)

14462039776828769318…95088844972920012799

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 #2,992,105

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