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Block #232,599

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2013, 5:23:27 AM Β· Difficulty 9.9412 Β· 6,599,458 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7cbacbc5390f71fb140e7e410ea5759f39b8addf9a9aac85a549c54a34e693de
View on Chainz β†—

Height

#232,599

Difficulty

9.941235

Transactions

1

Size

198 B

Version

2

Bits

09f0f4c7

Nonce

39,689

Timestamp

10/29/2013, 5:23:27 AM

Confirmations

6,599,458

Merkle Root

e3a33b2e5e4c13e2bf6a57611d4b98ec22aa1a7843c793be67054b702fab327b
Transactions (1)
Coinbasee3a33b2e5e4c13…054b702fab327b
1 in β†’ 1 out10.1000 XPM109 B
ARaPyHgj…nA9veLYH
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.

1.489 Γ— 10⁹²(93-digit number)
14895965317767061889…30416604761162636800
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
1.489 Γ— 10⁹²(93-digit number)
14895965317767061889…30416604761162636801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.979 Γ— 10⁹²(93-digit number)
29791930635534123778…60833209522325273601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.958 Γ— 10⁹²(93-digit number)
59583861271068247556…21666419044650547201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.191 Γ— 10⁹³(94-digit number)
11916772254213649511…43332838089301094401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.383 Γ— 10⁹³(94-digit number)
23833544508427299022…86665676178602188801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.766 Γ— 10⁹³(94-digit number)
47667089016854598045…73331352357204377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.533 Γ— 10⁹³(94-digit number)
95334178033709196090…46662704714408755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.906 Γ— 10⁹⁴(95-digit number)
19066835606741839218…93325409428817510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.813 Γ— 10⁹⁴(95-digit number)
38133671213483678436…86650818857635020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.626 Γ— 10⁹⁴(95-digit number)
76267342426967356872…73301637715270041601
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 232599

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 7cbacbc5390f71fb140e7e410ea5759f39b8addf9a9aac85a549c54a34e693de

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 #232,599 on Chainz β†—
Circulating Supply:57,900,588 XPMΒ·at block #6,832,056 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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