Block #2,851,832

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/23/2018, 10:19:21 AM · Difficulty 11.7240 · 3,966,178 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1c3a58fed8afcdf2ca5170fc7039b7e16959be29c1889ad2217d2fa3db6ce0f

View on Chainz ↗

Height

#2,851,832

Difficulty

11.723972

Transactions

Size

17.15 KB

Version

Bits

0bb95633

Nonce

898,938,414

Timestamp

9/23/2018, 10:19:21 AM

Confirmations

3,966,178

Mined by

⛏️ P2SHAHCqRiiYsGBLdJTn1RgbQvEjnSsTvZoL28

Merkle Root

808e5daf62cae4a82dee43cb85ceb8773a23e07d2f47352af78ca170acc1f070

Transactions (4)

Coinbasebed2ab296796e8…53dfceda385857

1 in → 1 out7.4500 XPM110 B

AHCqRiiY…sTvZoL28

7fa3c4073dc7d6…0ece720493f1d3

3 in → 2 out147.8702 XPM523 B

AaCt2Z2e…QB2Doko7 AUZDDKwE…orxYkeaR

aa92c381a6306a…601e1a820882f2

110 in → 2 out2348.2577 XPM15.96 KB

ATENo9Yq…AD2YpgR6 AVa5dYbR…j5uZYCvt

115cc9dabd81ec…029659c8b083f4

3 in → 2 out10.3276 XPM488 B

AJEXcWyD…yqT2LUQT AV7eJoTN…pLyuARba

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.

2.127 × 10⁹⁷(98-digit number)

21270593308449538022…42193241381761187839

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

2.127 × 10⁹⁷(98-digit number)

21270593308449538022…42193241381761187839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.127 × 10⁹⁷(98-digit number)

21270593308449538022…42193241381761187841

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

4.254 × 10⁹⁷(98-digit number)

42541186616899076044…84386482763522375679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.254 × 10⁹⁷(98-digit number)

42541186616899076044…84386482763522375681

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

8.508 × 10⁹⁷(98-digit number)

85082373233798152089…68772965527044751359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.508 × 10⁹⁷(98-digit number)

85082373233798152089…68772965527044751361

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

1.701 × 10⁹⁸(99-digit number)

17016474646759630417…37545931054089502719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.701 × 10⁹⁸(99-digit number)

17016474646759630417…37545931054089502721

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

3.403 × 10⁹⁸(99-digit number)

34032949293519260835…75091862108179005439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.403 × 10⁹⁸(99-digit number)

34032949293519260835…75091862108179005441

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

6.806 × 10⁹⁸(99-digit number)

68065898587038521671…50183724216358010879

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 #2,851,832

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