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Block #267,109

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/20/2013, 11:54:53 PM Β· Difficulty 9.9597 Β· 6,533,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d953fcbe8804286370f7aa4aef4bb835a4ed71afbac62341cb4f683b4788602
View on Chainz β†—

Height

#267,109

Difficulty

9.959734

Transactions

1

Size

199 B

Version

2

Bits

09f5b127

Nonce

71,231

Timestamp

11/20/2013, 11:54:53 PM

Confirmations

6,533,209

Merkle Root

5302560a115f5ba9a788c370153c1e6f30b6ef28f908482888cd5a539e6fcb9b
Transactions (1)
Coinbase5302560a115f5b…cd5a539e6fcb9b
1 in β†’ 1 out10.0700 XPM109 B
ATwT5Tp6…gFmG6Tgk
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.

1.076 Γ— 10⁹⁴(95-digit number)
10764670020031072987…73598146311671987200
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
1.076 Γ— 10⁹⁴(95-digit number)
10764670020031072987…73598146311671987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.152 Γ— 10⁹⁴(95-digit number)
21529340040062145975…47196292623343974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.305 Γ— 10⁹⁴(95-digit number)
43058680080124291950…94392585246687948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.611 Γ— 10⁹⁴(95-digit number)
86117360160248583901…88785170493375897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.722 Γ— 10⁹⁡(96-digit number)
17223472032049716780…77570340986751795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.444 Γ— 10⁹⁡(96-digit number)
34446944064099433560…55140681973503590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.889 Γ— 10⁹⁡(96-digit number)
68893888128198867121…10281363947007180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.377 Γ— 10⁹⁢(97-digit number)
13778777625639773424…20562727894014361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.755 Γ— 10⁹⁢(97-digit number)
27557555251279546848…41125455788028723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.511 Γ— 10⁹⁢(97-digit number)
55115110502559093697…82250911576057446401
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 267109

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 9d953fcbe8804286370f7aa4aef4bb835a4ed71afbac62341cb4f683b4788602

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 #267,109 on Chainz β†—
Circulating Supply:57,646,609 XPMΒ·at block #6,800,317 Β· updates every 60s
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