Block #3,045,765

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/9/2019, 4:07:42 PM · Difficulty 10.9961 · 3,795,768 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5b3bbab6e9a93eb22e6b648ef5617818cb0866c2365a37713c05903983d9a2b

View on Chainz ↗

Height

#3,045,765

Difficulty

10.996092

Transactions

Size

2.88 KB

Version

Bits

0afeffdc

Nonce

858,772,066

Timestamp

2/9/2019, 4:07:42 PM

Confirmations

3,795,768

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

bacd4fe26bd6e36d2025cee2b1fecd79cd9fffab5046508fa8d627d611f12330

Transactions (2)

Coinbase722e2399bcd0f7…70737e8e72595a

1 in → 1 out8.2900 XPM110 B

AUhjokok…k5m93PZR

fc07f34815e40a…dc16ba25c8aa5d

18 in → 2 out4155.4866 XPM2.68 KB

AQ8yeLcM…Ez9DfkNh AJor5KA8…3LSjzSo7

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.

1.573 × 10⁹⁸(99-digit number)

15738083152823002157…34530491410399887359

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

1.573 × 10⁹⁸(99-digit number)

15738083152823002157…34530491410399887359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.573 × 10⁹⁸(99-digit number)

15738083152823002157…34530491410399887361

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

3.147 × 10⁹⁸(99-digit number)

31476166305646004314…69060982820799774719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.147 × 10⁹⁸(99-digit number)

31476166305646004314…69060982820799774721

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

6.295 × 10⁹⁸(99-digit number)

62952332611292008629…38121965641599549439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.295 × 10⁹⁸(99-digit number)

62952332611292008629…38121965641599549441

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

1.259 × 10⁹⁹(100-digit number)

12590466522258401725…76243931283199098879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.259 × 10⁹⁹(100-digit number)

12590466522258401725…76243931283199098881

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

2.518 × 10⁹⁹(100-digit number)

25180933044516803451…52487862566398197759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.518 × 10⁹⁹(100-digit number)

25180933044516803451…52487862566398197761

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

5.036 × 10⁹⁹(100-digit number)

50361866089033606903…04975725132796395519

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 #3,045,765

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