Block #2,281,776

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/4/2017, 7:40:08 AM · Difficulty 10.9555 · 4,549,506 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93fbe8ee8a55bb89199d2195bb5138ea12725478b5f71abd9fd1f1f628b89b01

View on Chainz ↗

Height

#2,281,776

Difficulty

10.955501

Transactions

Size

765 B

Version

Bits

0af49bbe

Nonce

1,095,344,555

Timestamp

9/4/2017, 7:40:08 AM

Confirmations

4,549,506

Mined by

⛏️ P2SHASWjsb2KTQif2GN1qkGifZAk1KrV5J5X67

Merkle Root

33ce3d8aa5fdfedfb1036d483f4ef385f171da6e8039b874987fd9d1795fd0b8

Transactions (3)

Coinbase46949b7b7ae36b…157a6effbf3681

1 in → 1 out8.3400 XPM109 B

ASWjsb2K…rV5J5X67

a26e75d466dcd7…e18f8c3e7538fb

2 in → 2 out15.6102 XPM340 B

AQEfWikv…AFFvFEyz AcpAwkJX…1S4CVUW4

a3d2a580f942f2…837537ff1e52aa

1 in → 2 out4.1586 XPM226 B

AJY8WoNm…xnXHCxVr ALdDPtw1…JCnpMCdx

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.

5.866 × 10⁹⁴(95-digit number)

58662513349354951009…67012836204851281919

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

5.866 × 10⁹⁴(95-digit number)

58662513349354951009…67012836204851281919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.866 × 10⁹⁴(95-digit number)

58662513349354951009…67012836204851281921

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

1.173 × 10⁹⁵(96-digit number)

11732502669870990201…34025672409702563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.173 × 10⁹⁵(96-digit number)

11732502669870990201…34025672409702563841

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

2.346 × 10⁹⁵(96-digit number)

23465005339741980403…68051344819405127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.346 × 10⁹⁵(96-digit number)

23465005339741980403…68051344819405127681

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

4.693 × 10⁹⁵(96-digit number)

46930010679483960807…36102689638810255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.693 × 10⁹⁵(96-digit number)

46930010679483960807…36102689638810255361

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

9.386 × 10⁹⁵(96-digit number)

93860021358967921615…72205379277620510719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.386 × 10⁹⁵(96-digit number)

93860021358967921615…72205379277620510721

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

1.877 × 10⁹⁶(97-digit number)

18772004271793584323…44410758555241021439

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 #2,281,776

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