XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,006,677

Block #2,006,677

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2017, 10:44:36 AM Β· Difficulty 10.7105 Β· 4,830,373 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
6e16c617691f1f02be3591bbaf6a85f70bbc9a8f971fc9ebb0342b4cd5397211
View on Chainz β†—

Difficulty

10.710550

Transactions

1

Size

199 B

Version

2

Bits

0ab5e695

Nonce

700,947,570

Timestamp

3/3/2017, 10:44:36 AM

Confirmations

4,830,373

Merkle Root

6f596c9edbf3dbdd5f2b18c1877e717162f174127134713d8003b5932914f22f
Transactions (1)
Coinbase6f596c9edbf3db…03b5932914f22f
1 in β†’ 1 out8.7000 XPM109 B
ATAovv8F…k1sLRS4u
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.

1.137 Γ— 10⁹⁡(96-digit number)
11378554151543926308…73156183380000080460
Discovered Prime Numbers
p_k = 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.

1
origin + 1
1.137 Γ— 10⁹⁡(96-digit number)
11378554151543926308…73156183380000080461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.275 Γ— 10⁹⁡(96-digit number)
22757108303087852617…46312366760000160921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.551 Γ— 10⁹⁡(96-digit number)
45514216606175705235…92624733520000321841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.102 Γ— 10⁹⁡(96-digit number)
91028433212351410470…85249467040000643681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.820 Γ— 10⁹⁢(97-digit number)
18205686642470282094…70498934080001287361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.641 Γ— 10⁹⁢(97-digit number)
36411373284940564188…40997868160002574721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.282 Γ— 10⁹⁢(97-digit number)
72822746569881128376…81995736320005149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.456 Γ— 10⁹⁷(98-digit number)
14564549313976225675…63991472640010298881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.912 Γ— 10⁹⁷(98-digit number)
29129098627952451350…27982945280020597761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.825 Γ— 10⁹⁷(98-digit number)
58258197255904902700…55965890560041195521
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2006677

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 6e16c617691f1f02be3591bbaf6a85f70bbc9a8f971fc9ebb0342b4cd5397211

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 #2,006,677 on Chainz β†—
Circulating Supply:57,940,703 XPMΒ·at block #6,837,049 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