Block #2,166,716

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/19/2017, 2:20:31 AM · Difficulty 10.8979 · 4,660,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a720d0c2677427dbda3a2ef2102db522fd27f8d6f44a75358ebcbdc9675225cf

View on Chainz ↗

Height

#2,166,716

Difficulty

10.897851

Transactions

Size

2.19 KB

Version

Bits

0ae5d996

Nonce

1,187,927,722

Timestamp

6/19/2017, 2:20:31 AM

Confirmations

4,660,591

Mined by

⛏️ P2SHAM47ogKv543tnWVT7RSyUixETaCpgdzWM1

Merkle Root

56d92c3cf500ca63bac1bde6d8f6dd3d543016eac483aecc75bff0620eee9bd5

Transactions (4)

Coinbase89803dcbd9ac11…2607da20c368c5

1 in → 1 out8.4500 XPM110 B

AM47ogKv…CpgdzWM1

15e4a261d11c2b…dd03a1874f62bb

10 in → 3 out16705.5018 XPM1.56 KB

ARYYVuSH…ia6JaYta AdjPmM9R…JvHJQSGm AKJhEKQv…RiDdfqa2

2245492285133a…b9e1597a17bea3

1 in → 2 out207867.3448 XPM226 B

AP5mXfg7…qi3rLpKk AQMaJjtt…YyG7d84s

0857d666160748…319463071c5760

1 in → 2 out76470.1376 XPM227 B

AG1Mikd7…1bFFMJT5 AXWY9K4m…rrU9i9q7

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.

1.226 × 10⁹³(94-digit number)

12265521104122752874…90037616838685631039

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

1.226 × 10⁹³(94-digit number)

12265521104122752874…90037616838685631039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.226 × 10⁹³(94-digit number)

12265521104122752874…90037616838685631041

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

2.453 × 10⁹³(94-digit number)

24531042208245505748…80075233677371262079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.453 × 10⁹³(94-digit number)

24531042208245505748…80075233677371262081

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

4.906 × 10⁹³(94-digit number)

49062084416491011497…60150467354742524159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.906 × 10⁹³(94-digit number)

49062084416491011497…60150467354742524161

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

9.812 × 10⁹³(94-digit number)

98124168832982022995…20300934709485048319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.812 × 10⁹³(94-digit number)

98124168832982022995…20300934709485048321

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

1.962 × 10⁹⁴(95-digit number)

19624833766596404599…40601869418970096639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.962 × 10⁹⁴(95-digit number)

19624833766596404599…40601869418970096641

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 #2,166,716

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