XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #266,397

Block #266,397

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/20/2013, 10:04:49 AM Β· Difficulty 9.9607 Β· 6,533,769 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f093b1bea2db38838469856e82d12edeb682f11a0c0a7225f4a4a5db9524c175
View on Chainz β†—

Height

#266,397

Difficulty

9.960653

Transactions

1

Size

197 B

Version

2

Bits

09f5ed55

Nonce

406,702

Timestamp

11/20/2013, 10:04:49 AM

Confirmations

6,533,769

Merkle Root

2e403122c1215cffae09014a0a239fff7c806a8d96231b9a40e7148dbcbcb560
Transactions (1)
Coinbase2e403122c1215c…e7148dbcbcb560
1 in β†’ 1 out10.0600 XPM109 B
ALpZenv4…zxZZDJuw
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.

4.229 Γ— 10⁹⁰(91-digit number)
42292109410480628812…82373646926408607500
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
4.229 Γ— 10⁹⁰(91-digit number)
42292109410480628812…82373646926408607499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.458 Γ— 10⁹⁰(91-digit number)
84584218820961257624…64747293852817214999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.691 Γ— 10⁹¹(92-digit number)
16916843764192251524…29494587705634429999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.383 Γ— 10⁹¹(92-digit number)
33833687528384503049…58989175411268859999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.766 Γ— 10⁹¹(92-digit number)
67667375056769006099…17978350822537719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.353 Γ— 10⁹²(93-digit number)
13533475011353801219…35956701645075439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.706 Γ— 10⁹²(93-digit number)
27066950022707602439…71913403290150879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.413 Γ— 10⁹²(93-digit number)
54133900045415204879…43826806580301759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.082 Γ— 10⁹³(94-digit number)
10826780009083040975…87653613160603519999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 266397

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 f093b1bea2db38838469856e82d12edeb682f11a0c0a7225f4a4a5db9524c175

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 #266,397 on Chainz β†—
Circulating Supply:57,645,395 XPMΒ·at block #6,800,165 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK