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Home/Chain Registry/Block #2,109,405

Block #2,109,405

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2017, 3:46:03 AM Β· Difficulty 10.9001 Β· 4,727,500 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8c52ce984bd1ffb661fac0b0cb39300b37d7ff7c792d04f1b8671c56fd707bc5
View on Chainz β†—

Difficulty

10.900123

Transactions

2

Size

960 B

Version

2

Bits

0ae66e6f

Nonce

359,369,046

Timestamp

5/10/2017, 3:46:03 AM

Confirmations

4,727,500

Merkle Root

6159940d50aff28c0f3ea46db0ffc432825ca672671eb6410a7ac438d0fb980f
Transactions (2)
Coinbase7f7bd77b1dd99f…37e947510a1638
1 in β†’ 1 out8.4100 XPM109 B
Ab8Rf1Yc…63s5DPDy
d744186c059a7d…cb4592cea50c7a
6 in β†’ 2 out50.6600 XPM761 B
AQhSxeuH…opAjATYAAHbyumek…ry7WXVsp
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.849 Γ— 10⁹⁴(95-digit number)
58496551303944471788…70331699519968501760
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.849 Γ— 10⁹⁴(95-digit number)
58496551303944471788…70331699519968501759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.849 Γ— 10⁹⁴(95-digit number)
58496551303944471788…70331699519968501761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.169 Γ— 10⁹⁡(96-digit number)
11699310260788894357…40663399039937003519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.169 Γ— 10⁹⁡(96-digit number)
11699310260788894357…40663399039937003521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.339 Γ— 10⁹⁡(96-digit number)
23398620521577788715…81326798079874007039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.339 Γ— 10⁹⁡(96-digit number)
23398620521577788715…81326798079874007041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.679 Γ— 10⁹⁡(96-digit number)
46797241043155577431…62653596159748014079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.679 Γ— 10⁹⁡(96-digit number)
46797241043155577431…62653596159748014081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.359 Γ— 10⁹⁡(96-digit number)
93594482086311154862…25307192319496028159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.359 Γ— 10⁹⁡(96-digit number)
93594482086311154862…25307192319496028161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 2109405

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 8c52ce984bd1ffb661fac0b0cb39300b37d7ff7c792d04f1b8671c56fd707bc5

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 β†’ Debug Window β†’ 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 #2,109,405 on Chainz β†—
Circulating Supply:57,939,532 XPMΒ·at block #6,836,904 Β· updates every 60s
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