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Home/Chain Registry/Block #2,006,959

Block #2,006,959

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2017, 4:20:07 PM Β· Difficulty 10.7078 Β· 4,831,686 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eac3bb868a79405a5f54a65b6ce30ebbb34fa225279f2f33b91d690f47d3e306
View on Chainz β†—

Difficulty

10.707762

Transactions

2

Size

4.72 KB

Version

2

Bits

0ab52fde

Nonce

1,427,718,706

Timestamp

3/3/2017, 4:20:07 PM

Confirmations

4,831,686

Merkle Root

392c1c61dc709d782c2110b1c6307a5e729f3c5cfa607718dc222e64b09ee2dd
Transactions (2)
Coinbase5247410da0413b…2497f558b272e8
1 in β†’ 1 out8.7600 XPM110 B
AVySifdc…EzXFXWKU
689390b9335aba…64c13072ec8125
31 in β†’ 1 out80.1045 XPM4.53 KB
AUwo1vZj…93qAT7rY
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.

2.252 Γ— 10⁹⁡(96-digit number)
22520969344674009600…71251733760988087680
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
2.252 Γ— 10⁹⁡(96-digit number)
22520969344674009600…71251733760988087681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.504 Γ— 10⁹⁡(96-digit number)
45041938689348019200…42503467521976175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.008 Γ— 10⁹⁡(96-digit number)
90083877378696038401…85006935043952350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.801 Γ— 10⁹⁢(97-digit number)
18016775475739207680…70013870087904701441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.603 Γ— 10⁹⁢(97-digit number)
36033550951478415360…40027740175809402881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.206 Γ— 10⁹⁢(97-digit number)
72067101902956830721…80055480351618805761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.441 Γ— 10⁹⁷(98-digit number)
14413420380591366144…60110960703237611521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.882 Γ— 10⁹⁷(98-digit number)
28826840761182732288…20221921406475223041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.765 Γ— 10⁹⁷(98-digit number)
57653681522365464576…40443842812950446081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.153 Γ— 10⁹⁸(99-digit number)
11530736304473092915…80887685625900892161
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 2006959

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 eac3bb868a79405a5f54a65b6ce30ebbb34fa225279f2f33b91d690f47d3e306

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 #2,006,959 on Chainz β†—
Circulating Supply:57,953,425 XPMΒ·at block #6,838,644 Β· updates every 60s
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