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Home/Chain Registry/Block #423,835

Block #423,835

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/28/2014, 5:10:12 PM Β· Difficulty 10.3772 Β· 6,401,048 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b977868ae2ba115eec4b18c53c1b0822bb602cd6a400752ca1dd7c4d252e6bfe
View on Chainz β†—

Height

#423,835

Difficulty

10.377248

Transactions

1

Size

223 B

Version

2

Bits

0a609354

Nonce

239,449

Timestamp

2/28/2014, 5:10:12 PM

Confirmations

6,401,048

Merkle Root

85df60b3d13eeed0b05cfffe98b95b88e67101abd6694e2e497ddea1f2440a5a
Transactions (1)
Coinbase85df60b3d13eee…7ddea1f2440a5a
1 in β†’ 2 out9.2700 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

5.657 Γ— 10⁹⁸(99-digit number)
56576717274551561616…75352759412780241260
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
5.657 Γ— 10⁹⁸(99-digit number)
56576717274551561616…75352759412780241261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.131 Γ— 10⁹⁹(100-digit number)
11315343454910312323…50705518825560482521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.263 Γ— 10⁹⁹(100-digit number)
22630686909820624646…01411037651120965041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.526 Γ— 10⁹⁹(100-digit number)
45261373819641249293…02822075302241930081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.052 Γ— 10⁹⁹(100-digit number)
90522747639282498586…05644150604483860161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.810 Γ— 10¹⁰⁰(101-digit number)
18104549527856499717…11288301208967720321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.620 Γ— 10¹⁰⁰(101-digit number)
36209099055712999434…22576602417935440641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.241 Γ— 10¹⁰⁰(101-digit number)
72418198111425998869…45153204835870881281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.448 Γ— 10¹⁰¹(102-digit number)
14483639622285199773…90306409671741762561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.896 Γ— 10¹⁰¹(102-digit number)
28967279244570399547…80612819343483525121
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 423835

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 b977868ae2ba115eec4b18c53c1b0822bb602cd6a400752ca1dd7c4d252e6bfe

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 #423,835 on Chainz β†—
Circulating Supply:57,843,146 XPMΒ·at block #6,824,882 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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