XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,646,146

Block #2,646,146

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 5:36:17 AM Β· Difficulty 11.7453 Β· 4,187,468 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2c94ec7233f152358b67750b524c89cfe63765f9eafe1dd393640fec5f3d86d0
View on Chainz β†—

Difficulty

11.745296

Transactions

2

Size

428 B

Version

2

Bits

0bbecbb8

Nonce

2,010,590,132

Timestamp

5/3/2018, 5:36:17 AM

Confirmations

4,187,468

Merkle Root

5c02a3d34403a114477f886d3fbec5267e10c488e0616301f2059aa05885fc8f
Transactions (2)
Coinbasea257856d25562a…fc3fea15c522ba
1 in β†’ 1 out7.2500 XPM110 B
Adqah8zh…1WwoHJ9t
e206646cc303ac…8c33bca160b141
1 in β†’ 2 out164727.1887 XPM226 B
AUAVt7K1…iZdbcqDuARJu8krJ…m6tCoLRj
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.

7.147 Γ— 10⁹⁸(99-digit number)
71475198871903752946…03044091429302927360
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
7.147 Γ— 10⁹⁸(99-digit number)
71475198871903752946…03044091429302927359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.147 Γ— 10⁹⁸(99-digit number)
71475198871903752946…03044091429302927361
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
1.429 Γ— 10⁹⁹(100-digit number)
14295039774380750589…06088182858605854719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.429 Γ— 10⁹⁹(100-digit number)
14295039774380750589…06088182858605854721
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
2.859 Γ— 10⁹⁹(100-digit number)
28590079548761501178…12176365717211709439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.859 Γ— 10⁹⁹(100-digit number)
28590079548761501178…12176365717211709441
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
5.718 Γ— 10⁹⁹(100-digit number)
57180159097523002356…24352731434423418879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.718 Γ— 10⁹⁹(100-digit number)
57180159097523002356…24352731434423418881
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
1.143 Γ— 10¹⁰⁰(101-digit number)
11436031819504600471…48705462868846837759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.143 Γ— 10¹⁰⁰(101-digit number)
11436031819504600471…48705462868846837761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.287 Γ— 10¹⁰⁰(101-digit number)
22872063639009200942…97410925737693675519
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.287 Γ— 10¹⁰⁰(101-digit number)
22872063639009200942…97410925737693675521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2646146

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 2c94ec7233f152358b67750b524c89cfe63765f9eafe1dd393640fec5f3d86d0

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 #2,646,146 on Chainz β†—
Circulating Supply:57,913,122 XPMΒ·at block #6,833,613 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy