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Block #262,478

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2013, 9:37:09 PM Β· Difficulty 9.9685 Β· 6,550,350 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a881dc9ed95f6c48ecf2f7f7daa3d4c671b653cacd77b230c4e91e1c933922e1
View on Chainz β†—

Height

#262,478

Difficulty

9.968539

Transactions

1

Size

228 B

Version

2

Bits

09f7f234

Nonce

14,267

Timestamp

11/16/2013, 9:37:09 PM

Confirmations

6,550,350

Merkle Root

55374062a3251122573c6ef69d859ba0521bbf3ef9988b757fc789c8b206968d
Transactions (1)
Coinbase55374062a32511…c789c8b206968d
1 in β†’ 2 out10.0500 XPM137 B
AKcbk49N…GJbKa7j1ASNt3cJa…L5zCqAYM
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.

2.870 Γ— 10⁹⁢(97-digit number)
28703142225214462232…96644347606558747800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.870 Γ— 10⁹⁢(97-digit number)
28703142225214462232…96644347606558747799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.740 Γ— 10⁹⁢(97-digit number)
57406284450428924464…93288695213117495599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁷(98-digit number)
11481256890085784892…86577390426234991199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.296 Γ— 10⁹⁷(98-digit number)
22962513780171569785…73154780852469982399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.592 Γ— 10⁹⁷(98-digit number)
45925027560343139571…46309561704939964799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.185 Γ— 10⁹⁷(98-digit number)
91850055120686279142…92619123409879929599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.837 Γ— 10⁹⁸(99-digit number)
18370011024137255828…85238246819759859199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.674 Γ— 10⁹⁸(99-digit number)
36740022048274511657…70476493639519718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.348 Γ— 10⁹⁸(99-digit number)
73480044096549023314…40952987279039436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.469 Γ— 10⁹⁹(100-digit number)
14696008819309804662…81905974558078873599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 262478

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 a881dc9ed95f6c48ecf2f7f7daa3d4c671b653cacd77b230c4e91e1c933922e1

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 #262,478 on Chainz β†—
Circulating Supply:57,746,671 XPMΒ·at block #6,812,827 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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