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Block #265,355

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 11:55:08 AM Β· Difficulty 9.9628 Β· 6,560,016 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
edc417b82f0247b448148fd020d78225f4e5dc363d9734bb6e394ffef2cfda56
View on Chainz β†—

Height

#265,355

Difficulty

9.962792

Transactions

1

Size

207 B

Version

2

Bits

09f67989

Nonce

15,933

Timestamp

11/19/2013, 11:55:08 AM

Confirmations

6,560,016

Merkle Root

b975313bbd8ad74beef55ec062580459d76c7292715bc2fc28f99506dfbe5da7
Transactions (1)
Coinbaseb975313bbd8ad7…f99506dfbe5da7
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.617 Γ— 10⁹⁷(98-digit number)
86176564680257690449…45858517017343073320
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
8.617 Γ— 10⁹⁷(98-digit number)
86176564680257690449…45858517017343073321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.723 Γ— 10⁹⁸(99-digit number)
17235312936051538089…91717034034686146641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.447 Γ— 10⁹⁸(99-digit number)
34470625872103076179…83434068069372293281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.894 Γ— 10⁹⁸(99-digit number)
68941251744206152359…66868136138744586561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.378 Γ— 10⁹⁹(100-digit number)
13788250348841230471…33736272277489173121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.757 Γ— 10⁹⁹(100-digit number)
27576500697682460943…67472544554978346241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.515 Γ— 10⁹⁹(100-digit number)
55153001395364921887…34945089109956692481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.103 Γ— 10¹⁰⁰(101-digit number)
11030600279072984377…69890178219913384961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.206 Γ— 10¹⁰⁰(101-digit number)
22061200558145968755…39780356439826769921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.412 Γ— 10¹⁰⁰(101-digit number)
44122401116291937510…79560712879653539841
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 265355

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 edc417b82f0247b448148fd020d78225f4e5dc363d9734bb6e394ffef2cfda56

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 #265,355 on Chainz β†—
Circulating Supply:57,847,065 XPMΒ·at block #6,825,370 Β· updates every 60s
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