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Home/Chain Registry/Block #2,281,871

Block #2,281,871

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2017, 9:11:39 AM Β· Difficulty 10.9555 Β· 4,558,231 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1cbb2128425df1c05f3b3b2b67cd6ca4cc8241abb2d157305358e953a41974df
View on Chainz β†—

Difficulty

10.955540

Transactions

1

Size

200 B

Version

2

Bits

0af49e3f

Nonce

426,466,446

Timestamp

9/4/2017, 9:11:39 AM

Confirmations

4,558,231

Merkle Root

e64c25953e7805a886e04db0f0b8c867a831fa09f9565b78127a3eb32cad698a
Transactions (1)
Coinbasee64c25953e7805…7a3eb32cad698a
1 in β†’ 1 out8.3200 XPM110 B
AWsLzLoY…8NFwQGRZ
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.

1.607 Γ— 10⁹⁡(96-digit number)
16076665416188075128…49589850475514491520
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
1.607 Γ— 10⁹⁡(96-digit number)
16076665416188075128…49589850475514491519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.215 Γ— 10⁹⁡(96-digit number)
32153330832376150256…99179700951028983039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.430 Γ— 10⁹⁡(96-digit number)
64306661664752300513…98359401902057966079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.286 Γ— 10⁹⁢(97-digit number)
12861332332950460102…96718803804115932159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.572 Γ— 10⁹⁢(97-digit number)
25722664665900920205…93437607608231864319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.144 Γ— 10⁹⁢(97-digit number)
51445329331801840410…86875215216463728639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁷(98-digit number)
10289065866360368082…73750430432927457279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁷(98-digit number)
20578131732720736164…47500860865854914559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.115 Γ— 10⁹⁷(98-digit number)
41156263465441472328…95001721731709829119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.231 Γ— 10⁹⁷(98-digit number)
82312526930882944656…90003443463419658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.646 Γ— 10⁹⁸(99-digit number)
16462505386176588931…80006886926839316479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2281871

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 1cbb2128425df1c05f3b3b2b67cd6ca4cc8241abb2d157305358e953a41974df

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 #2,281,871 on Chainz β†—
Circulating Supply:57,965,126 XPMΒ·at block #6,840,101 Β· updates every 60s
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