Block #2,110,962

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2017, 3:00:07 AM · Difficulty 10.9033 · 4,726,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2282e7e6ca88a4d1304812f59c015bf940b18150be974cc299d90307acfd2c5

View on Chainz ↗

Height

#2,110,962

Difficulty

10.903295

Transactions

Size

1.08 KB

Version

Bits

0ae73e54

Nonce

521,378,266

Timestamp

5/11/2017, 3:00:07 AM

Confirmations

4,726,214

Mined by

⛏️ P2SHAH8Lg8YcizgdVQJEsdhQZap7Lte7FAdgRt

Merkle Root

746c608562b275094f749f1f0c1c760b73d6dcfd90a039b2db8c907982e0bbff

Transactions (5)

Coinbase315d80bbffdb88…fb642150a4defc

1 in → 1 out8.4400 XPM109 B

AH8Lg8Yc…e7FAdgRt

180d5d3f235e61…5b7ce051956bff

1 in → 2 out75098.7646 XPM227 B

AXs3ch8j…KSBJb4Ds APMTspTX…fWNRSany

b47b602800afb1…df1a3e5add66c2

1 in → 2 out43798.4337 XPM226 B

APMTspTX…fWNRSany ASPeY2ii…ycBcf48R

3217109b98950e…6ba89d59cf50de

1 in → 2 out42808.4237 XPM225 B

AaMNHhEf…7NXW62qf APMTspTX…fWNRSany

52edfd716dc1d8…edd0f0178c8d44

1 in → 2 out40828.4137 XPM227 B

APMTspTX…fWNRSany AecbHoe1…QYeGyxa3

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.

3.583 × 10⁹⁶(97-digit number)

35831690955455428354…43330929404011379199

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

3.583 × 10⁹⁶(97-digit number)

35831690955455428354…43330929404011379199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.583 × 10⁹⁶(97-digit number)

35831690955455428354…43330929404011379201

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

7.166 × 10⁹⁶(97-digit number)

71663381910910856709…86661858808022758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.166 × 10⁹⁶(97-digit number)

71663381910910856709…86661858808022758401

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

1.433 × 10⁹⁷(98-digit number)

14332676382182171341…73323717616045516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.433 × 10⁹⁷(98-digit number)

14332676382182171341…73323717616045516801

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

2.866 × 10⁹⁷(98-digit number)

28665352764364342683…46647435232091033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.866 × 10⁹⁷(98-digit number)

28665352764364342683…46647435232091033601

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

5.733 × 10⁹⁷(98-digit number)

57330705528728685367…93294870464182067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.733 × 10⁹⁷(98-digit number)

57330705528728685367…93294870464182067201

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 #2,110,962

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