Block #2,633,996

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 5:21:54 PM · Difficulty 11.2171 · 4,202,812 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

646d2ea1e69d933154e737152e2ec62e5b647f3a86b7dc5a35f7d7be24d9f319

View on Chainz ↗

Height

#2,633,996

Difficulty

11.217118

Transactions

Size

2.45 KB

Version

Bits

0b379512

Nonce

1,759,952,954

Timestamp

4/28/2018, 5:21:54 PM

Confirmations

4,202,812

Mined by

⛏️ P2SHAdenRCYjZ41K4DnWS3fMiiyFCbd8ywP9DA

Merkle Root

f8990756c61398ced6e95dbe1cf950096e75556017471adc137a486199dc945b

Transactions (4)

Coinbase8d1d1d2f178aa6…bc9203e6628ce8

1 in → 1 out7.9700 XPM110 B

AdenRCYj…d8ywP9DA

9de3b5899df3c5…b632252af27bf5

1 in → 2 out255423.6115 XPM226 B

AYWuadmt…GiouT2B7 AR3St6fg…6rDM4Jdu

b6dfe8d39bc304…720949dd0b0074

12 in → 2 out116.1011 XPM1.81 KB

AYkHP8Ch…XZWkALxV AXw41EFU…61pSNJQP

c6687eff4b837c…5fa22ab785616f

1 in → 2 out255290.7785 XPM227 B

AeZsHC9F…sVTJMPBj AFv1C5du…2nWt45yJ

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.

2.732 × 10⁹⁴(95-digit number)

27320000989431684488…67276976965404925519

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

2.732 × 10⁹⁴(95-digit number)

27320000989431684488…67276976965404925519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.732 × 10⁹⁴(95-digit number)

27320000989431684488…67276976965404925521

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

5.464 × 10⁹⁴(95-digit number)

54640001978863368976…34553953930809851039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.464 × 10⁹⁴(95-digit number)

54640001978863368976…34553953930809851041

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

1.092 × 10⁹⁵(96-digit number)

10928000395772673795…69107907861619702079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.092 × 10⁹⁵(96-digit number)

10928000395772673795…69107907861619702081

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

2.185 × 10⁹⁵(96-digit number)

21856000791545347590…38215815723239404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.185 × 10⁹⁵(96-digit number)

21856000791545347590…38215815723239404161

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

4.371 × 10⁹⁵(96-digit number)

43712001583090695181…76431631446478808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.371 × 10⁹⁵(96-digit number)

43712001583090695181…76431631446478808321

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

8.742 × 10⁹⁵(96-digit number)

87424003166181390363…52863262892957616639

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 #2,633,996

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