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Home/Chain Registry/Block #2,141,741

Block #2,141,741

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2017, 11:36:47 AM Β· Difficulty 10.8732 Β· 4,703,595 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
258a2f97689c2a1207687ba503b2a8a61f5612d45003ebaa0c4e38ae7446d5dd
View on Chainz β†—

Difficulty

10.873210

Transactions

1

Size

199 B

Version

2

Bits

0adf8ab3

Nonce

1,622,535,850

Timestamp

6/2/2017, 11:36:47 AM

Confirmations

4,703,595

Merkle Root

02b7ddfe3c0f6de63ee3369c8832768932630d016bce3bca16987155f9f3bf41
Transactions (1)
Coinbase02b7ddfe3c0f6d…987155f9f3bf41
1 in β†’ 1 out8.4400 XPM109 B
AGWd6Q6K…dLKEoBkY
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.

2.610 Γ— 10⁹⁡(96-digit number)
26105788369390119167…00206157519734030080
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
2.610 Γ— 10⁹⁡(96-digit number)
26105788369390119167…00206157519734030079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.221 Γ— 10⁹⁡(96-digit number)
52211576738780238334…00412315039468060159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁢(97-digit number)
10442315347756047666…00824630078936120319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁢(97-digit number)
20884630695512095333…01649260157872240639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.176 Γ— 10⁹⁢(97-digit number)
41769261391024190667…03298520315744481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.353 Γ— 10⁹⁢(97-digit number)
83538522782048381335…06597040631488962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁷(98-digit number)
16707704556409676267…13194081262977925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.341 Γ— 10⁹⁷(98-digit number)
33415409112819352534…26388162525955850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.683 Γ— 10⁹⁷(98-digit number)
66830818225638705068…52776325051911700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁸(99-digit number)
13366163645127741013…05552650103823400959
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 2141741

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 258a2f97689c2a1207687ba503b2a8a61f5612d45003ebaa0c4e38ae7446d5dd

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 #2,141,741 on Chainz β†—
Circulating Supply:58,007,129 XPMΒ·at block #6,845,335 Β· updates every 60s
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