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Block #2,238,132

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 2:04:50 PM Β· Difficulty 10.9461 Β· 4,598,990 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a45a9dd254ecf36668ac685c1508968d271694ac1ffc693f411866271b99ff8
View on Chainz β†—

Difficulty

10.946097

Transactions

1

Size

201 B

Version

2

Bits

0af23364

Nonce

259,912,575

Timestamp

8/5/2017, 2:04:50 PM

Confirmations

4,598,990

Merkle Root

e27ddef94d742ccdbd0f7fe7620c7ef8d3d8e34451e3533623eb3ae4404084af
Transactions (1)
Coinbasee27ddef94d742c…eb3ae4404084af
1 in β†’ 1 out8.3300 XPM110 B
AWnMYr2N…Ce4Zn5TM
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.

6.030 Γ— 10⁹⁢(97-digit number)
60307338526101237183…22030835394702882560
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
6.030 Γ— 10⁹⁢(97-digit number)
60307338526101237183…22030835394702882561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.206 Γ— 10⁹⁷(98-digit number)
12061467705220247436…44061670789405765121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.412 Γ— 10⁹⁷(98-digit number)
24122935410440494873…88123341578811530241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.824 Γ— 10⁹⁷(98-digit number)
48245870820880989746…76246683157623060481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.649 Γ— 10⁹⁷(98-digit number)
96491741641761979493…52493366315246120961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.929 Γ— 10⁹⁸(99-digit number)
19298348328352395898…04986732630492241921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.859 Γ— 10⁹⁸(99-digit number)
38596696656704791797…09973465260984483841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.719 Γ— 10⁹⁸(99-digit number)
77193393313409583595…19946930521968967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.543 Γ— 10⁹⁹(100-digit number)
15438678662681916719…39893861043937935361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.087 Γ— 10⁹⁹(100-digit number)
30877357325363833438…79787722087875870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.175 Γ— 10⁹⁹(100-digit number)
61754714650727666876…59575444175751741441
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 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
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 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 2238132

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 2a45a9dd254ecf36668ac685c1508968d271694ac1ffc693f411866271b99ff8

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 #2,238,132 on Chainz β†—
Circulating Supply:57,941,285 XPMΒ·at block #6,837,121 Β· updates every 60s
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