Block #2,646,354

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 7:59:20 AM · Difficulty 11.7486 · 4,184,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5ac1053ce9bf2d1e504d5a83b82fb46ad494e36ee84b4f7b1a72849d167d261

View on Chainz ↗

Height

#2,646,354

Difficulty

11.748644

Transactions

Size

1.58 KB

Version

Bits

0bbfa720

Nonce

1,032,473,341

Timestamp

5/3/2018, 7:59:20 AM

Confirmations

4,184,766

Mined by

⛏️ P2SHALx2abbmaNxCcQX7zU162iRyCEAYMsr4s8

Merkle Root

89e1c4c8a78bb8dc580d5aed1f26c034edee28c09d3003bba43cd9b585cb7fb2

Transactions (4)

Coinbasef7a4e967285e07…8ffb28da9a4a49

1 in → 1 out7.2600 XPM109 B

ALx2abbm…AYMsr4s8

933028ebec39d7…5ce4fb5935f2c6

1 in → 2 out13.7477 XPM225 B

AP5vvtjG…DfN55S5j AUMAFvFG…U3tviQiX

8605170912a4ca…0e1a6cd5908aa6

2 in → 2 out26.4401 XPM373 B

AQCfpNso…ba6bkTVx AZ4UnHzJ…PH7NQioA

989ad688d1e114…eeebaf5993ffd6

5 in → 2 out4.0179 XPM819 B

AZNuaftZ…zxpqG1qd ANxNfXmZ…4p5PaHCM

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.

8.022 × 10⁹³(94-digit number)

80221944283336173552…39822057673001921279

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

8.022 × 10⁹³(94-digit number)

80221944283336173552…39822057673001921279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.022 × 10⁹³(94-digit number)

80221944283336173552…39822057673001921281

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

1.604 × 10⁹⁴(95-digit number)

16044388856667234710…79644115346003842559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.604 × 10⁹⁴(95-digit number)

16044388856667234710…79644115346003842561

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

3.208 × 10⁹⁴(95-digit number)

32088777713334469420…59288230692007685119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.208 × 10⁹⁴(95-digit number)

32088777713334469420…59288230692007685121

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

6.417 × 10⁹⁴(95-digit number)

64177555426668938841…18576461384015370239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.417 × 10⁹⁴(95-digit number)

64177555426668938841…18576461384015370241

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

1.283 × 10⁹⁵(96-digit number)

12835511085333787768…37152922768030740479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.283 × 10⁹⁵(96-digit number)

12835511085333787768…37152922768030740481

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

2.567 × 10⁹⁵(96-digit number)

25671022170667575536…74305845536061480959

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 #2,646,354

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