Block #2,180,170

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/27/2017, 1:51:32 AM · Difficulty 10.9311 · 4,645,974 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e59d0db17bdabd939b965572979726b901b417f059bc4cecc7542ba270b4aa8d

View on Chainz ↗

Height

#2,180,170

Difficulty

10.931123

Transactions

Size

1.94 KB

Version

Bits

0aee5e10

Nonce

49,341,299

Timestamp

6/27/2017, 1:51:32 AM

Confirmations

4,645,974

Mined by

⛏️ P2SHAZE33Zkhop8KbDXaU739Qhi9DkkF6cj1wZ

Merkle Root

09b2f88e5aefc373a37e67a894b7e26bb1290a5fbb64ba801badfa5ec6ab12dd

Transactions (3)

Coinbaseb52903312e41b8…c33cfd8e869348

1 in → 1 out8.3900 XPM110 B

AZE33Zkh…kF6cj1wZ

2a1928a4b4e8d8…8249dbb45857e2

9 in → 2 out558.8124 XPM1.38 KB

AKhxU9vu…RSAW9ny8 ARLxMe9N…Bxx8GE18

3c1fd57b1b49ee…cdcf0c17ea298c

2 in → 2 out262.0991 XPM375 B

AW91B7sf…Ke78fRVZ AZxSv1qo…psGzapJg

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.

2.468 × 10⁹³(94-digit number)

24684249736562225019…73020878105950234889

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

2.468 × 10⁹³(94-digit number)

24684249736562225019…73020878105950234889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.468 × 10⁹³(94-digit number)

24684249736562225019…73020878105950234891

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

4.936 × 10⁹³(94-digit number)

49368499473124450039…46041756211900469779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.936 × 10⁹³(94-digit number)

49368499473124450039…46041756211900469781

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

9.873 × 10⁹³(94-digit number)

98736998946248900078…92083512423800939559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.873 × 10⁹³(94-digit number)

98736998946248900078…92083512423800939561

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

1.974 × 10⁹⁴(95-digit number)

19747399789249780015…84167024847601879119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.974 × 10⁹⁴(95-digit number)

19747399789249780015…84167024847601879121

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

3.949 × 10⁹⁴(95-digit number)

39494799578499560031…68334049695203758239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.949 × 10⁹⁴(95-digit number)

39494799578499560031…68334049695203758241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,180,170

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