Block #2,110,190

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/10/2017, 2:50:07 PM · Difficulty 10.9025 · 4,735,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

144961a344c0ee9f89e6b51b013ba83a9969c28352bd1562578932ae1d2fca01

View on Chainz ↗

Height

#2,110,190

Difficulty

10.902455

Transactions

Size

1.58 KB

Version

Bits

0ae70745

Nonce

282,879,666

Timestamp

5/10/2017, 2:50:07 PM

Confirmations

4,735,067

Mined by

⛏️ P2SHAUqi3RibYBp5PQGKMTAhQiWWAdAGvDe64G

Merkle Root

c500a609bba2fa14a69311de4dce26fdfa1332284c5f7bfb82345253f18c847b

Transactions (4)

Coinbaseb716e89cb60b78…245347220de7c8

1 in → 1 out8.4300 XPM110 B

AUqi3Rib…AGvDe64G

39dd8a0618e3bf…458cea7479dd88

6 in → 2 out8.1600 XPM965 B

ANEMMbxx…yxibpPYi AU3fbvwD…o6CVVxTZ

0aa68f16a839ce…993aae7052763f

1 in → 2 out4.4000 XPM225 B

Af2J6BuG…H8ThkXpN ALXQbpau…QsqtGCai

ec8b1c4a358d08…9faa5617829398

1 in → 2 out4.4000 XPM226 B

Aes366sP…gwL7rjwi AH4gcCC7…1erJn7JT

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.

1.241 × 10⁹⁸(99-digit number)

12419296140920376269…75868978991218687999

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

1.241 × 10⁹⁸(99-digit number)

12419296140920376269…75868978991218687999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.241 × 10⁹⁸(99-digit number)

12419296140920376269…75868978991218688001

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

2.483 × 10⁹⁸(99-digit number)

24838592281840752538…51737957982437375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.483 × 10⁹⁸(99-digit number)

24838592281840752538…51737957982437376001

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

4.967 × 10⁹⁸(99-digit number)

49677184563681505077…03475915964874751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.967 × 10⁹⁸(99-digit number)

49677184563681505077…03475915964874752001

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

9.935 × 10⁹⁸(99-digit number)

99354369127363010155…06951831929749503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.935 × 10⁹⁸(99-digit number)

99354369127363010155…06951831929749504001

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

1.987 × 10⁹⁹(100-digit number)

19870873825472602031…13903663859499007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.987 × 10⁹⁹(100-digit number)

19870873825472602031…13903663859499008001

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

3.974 × 10⁹⁹(100-digit number)

39741747650945204062…27807327718998015999

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 #2,110,190

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