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Home/Chain Registry/Block #2,005,201

Block #2,005,201

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/2/2017, 6:59:37 AM Β· Difficulty 10.7214 Β· 4,837,198 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f357f77dd6e018ff8472a44789cf1ec42c2f214d699227180595fc45c4df0aae
View on Chainz β†—

Difficulty

10.721378

Transactions

1

Size

199 B

Version

2

Bits

0ab8ac3e

Nonce

1,820,112,241

Timestamp

3/2/2017, 6:59:37 AM

Confirmations

4,837,198

Merkle Root

dbd047080867cc14fddd93c780646ed0b2dd9c0c3024a746b9cd30085db5db94
Transactions (1)
Coinbasedbd047080867cc…cd30085db5db94
1 in β†’ 1 out8.6900 XPM109 B
AVcm9F3M…Z2WALGVG
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.

2.366 Γ— 10⁹⁴(95-digit number)
23668685570950379046…02169028025932847350
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.366 Γ— 10⁹⁴(95-digit number)
23668685570950379046…02169028025932847349
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.733 Γ— 10⁹⁴(95-digit number)
47337371141900758093…04338056051865694699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.467 Γ— 10⁹⁴(95-digit number)
94674742283801516187…08676112103731389399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁡(96-digit number)
18934948456760303237…17352224207462778799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.786 Γ— 10⁹⁡(96-digit number)
37869896913520606475…34704448414925557599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.573 Γ— 10⁹⁡(96-digit number)
75739793827041212950…69408896829851115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.514 Γ— 10⁹⁢(97-digit number)
15147958765408242590…38817793659702230399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.029 Γ— 10⁹⁢(97-digit number)
30295917530816485180…77635587319404460799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.059 Γ— 10⁹⁢(97-digit number)
60591835061632970360…55271174638808921599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.211 Γ— 10⁹⁷(98-digit number)
12118367012326594072…10542349277617843199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2005201

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 f357f77dd6e018ff8472a44789cf1ec42c2f214d699227180595fc45c4df0aae

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 #2,005,201 on Chainz β†—
Circulating Supply:57,983,604 XPMΒ·at block #6,842,398 Β· updates every 60s
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