Block #3,063,286

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/22/2019, 12:42:27 AM · Difficulty 11.0036 · 3,779,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b46a3224b805cf37ed7ca6715c356d38a303446096a94b85f70eeb41b2d66de9

View on Chainz ↗

Height

#3,063,286

Difficulty

11.003650

Transactions

Size

4.37 KB

Version

Bits

0b00ef2f

Nonce

1,037,049,243

Timestamp

2/22/2019, 12:42:27 AM

Confirmations

3,779,550

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

d748551c2cd4f3eb776c6804e4a62b774436cae90c6317a3e34168a3f75d19ad

Transactions (5)

Coinbaseea4dbaa0cd48d8…1ec082f564efc2

1 in → 1 out8.3300 XPM110 B

AbXwmGxD…4XXYP765

9a7d2d8cec52b9…dbb13e760d3e30

23 in → 2 out5000.0100 XPM3.40 KB

AUWLiCGG…uTwceacQ AdjSReTp…WUVuPaxW

d8e34cdf96239a…4f633ef3b55bf2

2 in → 2 out12.9361 XPM340 B

ASUcJnNi…eSt73bFU AbXwmGxD…4XXYP765

7ac891cf29bf94…f2dc5ccd961f0b

1 in → 2 out7.2085 XPM226 B

AbXwmGxD…4XXYP765 AVL7GXLb…at8P37UX

b07a7f0c792c7c…3b19ac4dfcbfcb

1 in → 2 out3.1116 XPM226 B

AbXwmGxD…4XXYP765 AGbm9W17…Jvw6eg2t

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.

9.241 × 10⁹⁵(96-digit number)

92411142458860809565…17116883207283015679

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

9.241 × 10⁹⁵(96-digit number)

92411142458860809565…17116883207283015679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.241 × 10⁹⁵(96-digit number)

92411142458860809565…17116883207283015681

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

1.848 × 10⁹⁶(97-digit number)

18482228491772161913…34233766414566031359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.848 × 10⁹⁶(97-digit number)

18482228491772161913…34233766414566031361

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

3.696 × 10⁹⁶(97-digit number)

36964456983544323826…68467532829132062719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.696 × 10⁹⁶(97-digit number)

36964456983544323826…68467532829132062721

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

7.392 × 10⁹⁶(97-digit number)

73928913967088647652…36935065658264125439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.392 × 10⁹⁶(97-digit number)

73928913967088647652…36935065658264125441

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

1.478 × 10⁹⁷(98-digit number)

14785782793417729530…73870131316528250879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.478 × 10⁹⁷(98-digit number)

14785782793417729530…73870131316528250881

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

2.957 × 10⁹⁷(98-digit number)

29571565586835459061…47740262633056501759

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 #3,063,286

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