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Home/Chain Registry/Block #2,205,871

Block #2,205,871

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2017, 2:55:43 AM Β· Difficulty 10.9461 Β· 4,636,531 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ffcfac2777b5b2b589811bb9ca8f43da01059326a3e985b916080de8caf3a757
View on Chainz β†—

Difficulty

10.946066

Transactions

1

Size

200 B

Version

2

Bits

0af23167

Nonce

705,990,223

Timestamp

7/14/2017, 2:55:43 AM

Confirmations

4,636,531

Merkle Root

7e668bb972dcb9c7c75b5dae9ef45f31f28cd48af060f6263cbed4088b5c6331
Transactions (1)
Coinbase7e668bb972dcb9…bed4088b5c6331
1 in β†’ 1 out8.3300 XPM110 B
AMnBRKyV…xGpZoJRH
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.

1.247 Γ— 10⁹⁡(96-digit number)
12477163285164530344…79803116821375356800
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
1.247 Γ— 10⁹⁡(96-digit number)
12477163285164530344…79803116821375356799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.495 Γ— 10⁹⁡(96-digit number)
24954326570329060689…59606233642750713599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.990 Γ— 10⁹⁡(96-digit number)
49908653140658121378…19212467285501427199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.981 Γ— 10⁹⁡(96-digit number)
99817306281316242756…38424934571002854399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.996 Γ— 10⁹⁢(97-digit number)
19963461256263248551…76849869142005708799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.992 Γ— 10⁹⁢(97-digit number)
39926922512526497102…53699738284011417599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.985 Γ— 10⁹⁢(97-digit number)
79853845025052994205…07399476568022835199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.597 Γ— 10⁹⁷(98-digit number)
15970769005010598841…14798953136045670399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.194 Γ— 10⁹⁷(98-digit number)
31941538010021197682…29597906272091340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.388 Γ— 10⁹⁷(98-digit number)
63883076020042395364…59195812544182681599
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 2205871

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 ffcfac2777b5b2b589811bb9ca8f43da01059326a3e985b916080de8caf3a757

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 #2,205,871 on Chainz β†—
Circulating Supply:57,983,627 XPMΒ·at block #6,842,401 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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