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Block #411,196

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/19/2014, 2:07:27 PM Β· Difficulty 10.4313 Β· 6,390,033 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3943d9943ba74873d8d4ecfbe2b9e845dd5772483ce21661313b6d0592774a7f
View on Chainz β†—

Height

#411,196

Difficulty

10.431340

Transactions

1

Size

207 B

Version

2

Bits

0a6e6c49

Nonce

1,784

Timestamp

2/19/2014, 2:07:27 PM

Confirmations

6,390,033

Merkle Root

0faa999e7746fc4d3a85bb4c1acf15c8f17b2e96787c4600503c433d2fa791bb
Transactions (1)
Coinbase0faa999e7746fc…3c433d2fa791bb
1 in β†’ 1 out9.1800 XPM116 B
AbwWkWZt…kawDhufa
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.

1.093 Γ— 10⁹⁷(98-digit number)
10935225488267780533…92893623510668887320
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
1.093 Γ— 10⁹⁷(98-digit number)
10935225488267780533…92893623510668887321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.187 Γ— 10⁹⁷(98-digit number)
21870450976535561066…85787247021337774641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.374 Γ— 10⁹⁷(98-digit number)
43740901953071122133…71574494042675549281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.748 Γ— 10⁹⁷(98-digit number)
87481803906142244266…43148988085351098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.749 Γ— 10⁹⁸(99-digit number)
17496360781228448853…86297976170702197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.499 Γ— 10⁹⁸(99-digit number)
34992721562456897706…72595952341404394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.998 Γ— 10⁹⁸(99-digit number)
69985443124913795412…45191904682808788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.399 Γ— 10⁹⁹(100-digit number)
13997088624982759082…90383809365617576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.799 Γ— 10⁹⁹(100-digit number)
27994177249965518165…80767618731235153921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.598 Γ— 10⁹⁹(100-digit number)
55988354499931036330…61535237462470307841
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 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
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 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 411196

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 3943d9943ba74873d8d4ecfbe2b9e845dd5772483ce21661313b6d0592774a7f

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 #411,196 on Chainz β†—
Circulating Supply:57,653,897 XPMΒ·at block #6,801,228 Β· updates every 60s
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