Block #2,576,213

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/20/2018, 5:23:44 PM · Difficulty 10.9957 · 4,265,936 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa750661912cadee5bea29cd7d0a10fc90423f6f98482f9ef042936645aa2dd1

View on Chainz ↗

Height

#2,576,213

Difficulty

10.995668

Transactions

Size

1.52 KB

Version

Bits

0afee412

Nonce

365,023,096

Timestamp

3/20/2018, 5:23:44 PM

Confirmations

4,265,936

Mined by

⛏️ P2SHAeuDZXZ2wfETSLkrYkrnKoRAvdGVYch1yS

Merkle Root

da500ea9006465df73f4a147dcfd05b8f670fa4560b9bdb3733aa213f2fb0c22

Transactions (5)

Coinbase855623d9141e62…0efaa7ebb7cd64

1 in → 1 out8.3000 XPM110 B

AeuDZXZ2…GVYch1yS

bd97368b2784b4…0865bb3d756527

1 in → 2 out1.7155 XPM226 B

ATUV4rYM…N7NW9v2D AL32XFtF…buETRSdg

6ce31ba9349e16…318dc55791c63a

2 in → 2 out16.5100 XPM305 B

AcFTJJbj…pSs7etzL AMJq5v98…nvBEtQjJ

067c3e614279a2…8ae150e3b68b96

2 in → 2 out13.0200 XPM341 B

AQkVXXkB…wJGoQg3m APeWfxBA…tPg4LWgA

1c9964239cd9a8…c7bbd0bdabb4c9

3 in → 2 out10.2800 XPM487 B

AaD13FYh…2yiisheS AHZRKKFA…ELvY2MKQ

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.

2.006 × 10⁹⁴(95-digit number)

20068821129719497834…95316995141320928159

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

2.006 × 10⁹⁴(95-digit number)

20068821129719497834…95316995141320928159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.006 × 10⁹⁴(95-digit number)

20068821129719497834…95316995141320928161

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

4.013 × 10⁹⁴(95-digit number)

40137642259438995668…90633990282641856319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.013 × 10⁹⁴(95-digit number)

40137642259438995668…90633990282641856321

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

8.027 × 10⁹⁴(95-digit number)

80275284518877991336…81267980565283712639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.027 × 10⁹⁴(95-digit number)

80275284518877991336…81267980565283712641

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

1.605 × 10⁹⁵(96-digit number)

16055056903775598267…62535961130567425279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.605 × 10⁹⁵(96-digit number)

16055056903775598267…62535961130567425281

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

3.211 × 10⁹⁵(96-digit number)

32110113807551196534…25071922261134850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.211 × 10⁹⁵(96-digit number)

32110113807551196534…25071922261134850561

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

6.422 × 10⁹⁵(96-digit number)

64220227615102393069…50143844522269701119

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 #2,576,213

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