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Block #236,065

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 7:13:50 AM Β· Difficulty 9.9467 Β· 6,562,492 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c728a1da965a9fc57bf79aef3d28a84b37a659e42fd7105cae9de1449e4f29d
View on Chainz β†—

Height

#236,065

Difficulty

9.946663

Transactions

1

Size

198 B

Version

2

Bits

09f25888

Nonce

87,948

Timestamp

10/31/2013, 7:13:50 AM

Confirmations

6,562,492

Merkle Root

8438dad4f8bcac85240366b2d967bcbc1f91608758628cd5b8c6b75316ef4c9a
Transactions (1)
Coinbase8438dad4f8bcac…c6b75316ef4c9a
1 in β†’ 1 out10.0900 XPM109 B
AL2EWWZm…CwsD5iKb
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.

1.068 Γ— 10⁹³(94-digit number)
10684268042370626705…11567629908076182640
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
1.068 Γ— 10⁹³(94-digit number)
10684268042370626705…11567629908076182641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.136 Γ— 10⁹³(94-digit number)
21368536084741253411…23135259816152365281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.273 Γ— 10⁹³(94-digit number)
42737072169482506822…46270519632304730561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.547 Γ— 10⁹³(94-digit number)
85474144338965013644…92541039264609461121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.709 Γ— 10⁹⁴(95-digit number)
17094828867793002728…85082078529218922241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.418 Γ— 10⁹⁴(95-digit number)
34189657735586005457…70164157058437844481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.837 Γ— 10⁹⁴(95-digit number)
68379315471172010915…40328314116875688961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13675863094234402183…80656628233751377921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27351726188468804366…61313256467502755841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.470 Γ— 10⁹⁡(96-digit number)
54703452376937608732…22626512935005511681
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 236065

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 7c728a1da965a9fc57bf79aef3d28a84b37a659e42fd7105cae9de1449e4f29d

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 #236,065 on Chainz β†—
Circulating Supply:57,632,472 XPMΒ·at block #6,798,556 Β· updates every 60s
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