Home/Chain Registry/Block #2,110,040

Block #2,110,040

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2017, 12:45:33 PM · Difficulty 10.9020 · 4,729,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c97d80b7fceadd986304a19a9a0c4c6cd980c07c8592981f5eaa7655e4fb26f0

View on Chainz ↗

Height

#2,110,040

Difficulty

10.901956

Transactions

Size

584 B

Version

Bits

0ae6e69f

Nonce

290,700,944

Timestamp

5/10/2017, 12:45:33 PM

Confirmations

4,729,036

Merkle Root

83f9561f7f820ff2c6efa946119f3676d39b5ed79456b73caa0c31be081182c8

Transactions (3)

Coinbasefcb142320dc4be…e770b252e26783

1 in → 1 out8.4200 XPM110 B

AccL7GFG…VByimq1G

d1d370d0a38b20…dda5a8edce9af5

1 in → 2 out8.4100 XPM191 B

AGbm9W17…Jvw6eg2t AGPJShfF…HmMj8c3A

30902dea4799e2…cc729150dfd22a

1 in → 2 out8.4100 XPM192 B

AJG7CUuX…NLT3RPDB AXpQMVmt…N4y4jUJc

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.

8.650 × 10⁹⁷(98-digit number)

86505985108503769233…88029031378960875520

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

8.650 × 10⁹⁷(98-digit number)

86505985108503769233…88029031378960875519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.650 × 10⁹⁷(98-digit number)

86505985108503769233…88029031378960875521

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

1.730 × 10⁹⁸(99-digit number)

17301197021700753846…76058062757921751039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.730 × 10⁹⁸(99-digit number)

17301197021700753846…76058062757921751041

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

3.460 × 10⁹⁸(99-digit number)

34602394043401507693…52116125515843502079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.460 × 10⁹⁸(99-digit number)

34602394043401507693…52116125515843502081

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

6.920 × 10⁹⁸(99-digit number)

69204788086803015387…04232251031687004159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.920 × 10⁹⁸(99-digit number)

69204788086803015387…04232251031687004161

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

1.384 × 10⁹⁹(100-digit number)

13840957617360603077…08464502063374008319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.384 × 10⁹⁹(100-digit number)

13840957617360603077…08464502063374008321

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2110040

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock c97d80b7fceadd986304a19a9a0c4c6cd980c07c8592981f5eaa7655e4fb26f0

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,110,040 on Chainz ↗

Block #2,110,040

Cookie Preferences