XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #267,409

Block #267,409

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/21/2013, 6:43:41 AM Β· Difficulty 9.9589 Β· 6,528,594 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98e898be0864ae22aec90af673d951a4b0be5e4e23f159722d8e9870363a8a83
View on Chainz β†—

Height

#267,409

Difficulty

9.958888

Transactions

1

Size

201 B

Version

2

Bits

09f579b6

Nonce

464,978

Timestamp

11/21/2013, 6:43:41 AM

Confirmations

6,528,594

Merkle Root

542c10bcf0dd432ab33af7dcdb5777a32b14b8025ed4e0075fd4ff70a3d5d26d
Transactions (1)
Coinbase542c10bcf0dd43…d4ff70a3d5d26d
1 in β†’ 1 out10.0700 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.854 Γ— 10⁹⁢(97-digit number)
38541907976581127418…42675936149049943040
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
3.854 Γ— 10⁹⁢(97-digit number)
38541907976581127418…42675936149049943041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.708 Γ— 10⁹⁢(97-digit number)
77083815953162254836…85351872298099886081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.541 Γ— 10⁹⁷(98-digit number)
15416763190632450967…70703744596199772161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.083 Γ— 10⁹⁷(98-digit number)
30833526381264901934…41407489192399544321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.166 Γ— 10⁹⁷(98-digit number)
61667052762529803869…82814978384799088641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.233 Γ— 10⁹⁸(99-digit number)
12333410552505960773…65629956769598177281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.466 Γ— 10⁹⁸(99-digit number)
24666821105011921547…31259913539196354561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.933 Γ— 10⁹⁸(99-digit number)
49333642210023843095…62519827078392709121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.866 Γ— 10⁹⁸(99-digit number)
98667284420047686190…25039654156785418241
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 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
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 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 267409

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 98e898be0864ae22aec90af673d951a4b0be5e4e23f159722d8e9870363a8a83

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 #267,409 on Chainz β†—
Circulating Supply:57,612,113 XPMΒ·at block #6,796,002 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