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Block #264,658

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2013, 9:32:00 PM Β· Difficulty 9.9640 Β· 6,535,744 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00736e67087ddd85c8069cc459b5d13c634afe9bf8a03a05f10bb09f4674c8cc
View on Chainz β†—

Height

#264,658

Difficulty

9.963990

Transactions

2

Size

1.03 KB

Version

2

Bits

09f6c805

Nonce

28,333

Timestamp

11/18/2013, 9:32:00 PM

Confirmations

6,535,744

Merkle Root

419c1ec25ce270867c9809e2f3c274e366a7321c641db4794ba52e15b3073300
Transactions (2)
Coinbasebf7d107c818ad6…3058c5c76f91cd
1 in β†’ 2 out10.0700 XPM142 B
AdGRRh1e…QmctLb24AHsw4d6U…EnM8UXNZ
9fd258f3d982e3…27bf80573e0f87
5 in β†’ 2 out1.0100 XPM819 B
AaomdbCm…9zRVUacpARX57t8e…RJWav5Vy
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.

1.760 Γ— 10⁹⁢(97-digit number)
17601414283444047084…30903692045518630400
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
1.760 Γ— 10⁹⁢(97-digit number)
17601414283444047084…30903692045518630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.520 Γ— 10⁹⁢(97-digit number)
35202828566888094168…61807384091037260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.040 Γ— 10⁹⁢(97-digit number)
70405657133776188337…23614768182074521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.408 Γ— 10⁹⁷(98-digit number)
14081131426755237667…47229536364149043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.816 Γ— 10⁹⁷(98-digit number)
28162262853510475335…94459072728298086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.632 Γ— 10⁹⁷(98-digit number)
56324525707020950670…88918145456596172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.126 Γ— 10⁹⁸(99-digit number)
11264905141404190134…77836290913192345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.252 Γ— 10⁹⁸(99-digit number)
22529810282808380268…55672581826384691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.505 Γ— 10⁹⁸(99-digit number)
45059620565616760536…11345163652769382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.011 Γ— 10⁹⁸(99-digit number)
90119241131233521072…22690327305538764801
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 264658

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 00736e67087ddd85c8069cc459b5d13c634afe9bf8a03a05f10bb09f4674c8cc

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 #264,658 on Chainz β†—
Circulating Supply:57,647,278 XPMΒ·at block #6,800,401 Β· updates every 60s
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