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Block #264,534

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2013, 6:53:03 PM Β· Difficulty 9.9642 Β· 6,540,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4d4be497cd4d48d256b51a122fa308475234442e1f223a46338e3b08bd4b0e74
View on Chainz β†—

Height

#264,534

Difficulty

9.964214

Transactions

1

Size

208 B

Version

2

Bits

09f6d6b5

Nonce

144,176

Timestamp

11/18/2013, 6:53:03 PM

Confirmations

6,540,743

Merkle Root

c530ad725a3ccfc98fb36f9656aca2c803b9d5728c9888d7f11a4c4f586095ff
Transactions (1)
Coinbasec530ad725a3ccf…1a4c4f586095ff
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.

4.728 Γ— 10⁹⁹(100-digit number)
47283620546307999829…10388929308073656320
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
4.728 Γ— 10⁹⁹(100-digit number)
47283620546307999829…10388929308073656321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.456 Γ— 10⁹⁹(100-digit number)
94567241092615999659…20777858616147312641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.891 Γ— 10¹⁰⁰(101-digit number)
18913448218523199931…41555717232294625281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.782 Γ— 10¹⁰⁰(101-digit number)
37826896437046399863…83111434464589250561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.565 Γ— 10¹⁰⁰(101-digit number)
75653792874092799727…66222868929178501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.513 Γ— 10¹⁰¹(102-digit number)
15130758574818559945…32445737858357002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.026 Γ— 10¹⁰¹(102-digit number)
30261517149637119891…64891475716714004481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.052 Γ— 10¹⁰¹(102-digit number)
60523034299274239782…29782951433428008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.210 Γ— 10¹⁰²(103-digit number)
12104606859854847956…59565902866856017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.420 Γ— 10¹⁰²(103-digit number)
24209213719709695912…19131805733712035841
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 264534

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 4d4be497cd4d48d256b51a122fa308475234442e1f223a46338e3b08bd4b0e74

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 #264,534 on Chainz β†—
Circulating Supply:57,686,288 XPMΒ·at block #6,805,276 Β· updates every 60s
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