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Block #274,160

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/26/2013, 4:23:16 AM Β· Difficulty 9.9565 Β· 6,522,229 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01bed5f6e0829642bb21c5fb700cd492bc80cfcf3fb33406235599366d0bd608
View on Chainz β†—

Height

#274,160

Difficulty

9.956525

Transactions

1

Size

206 B

Version

2

Bits

09f4ded8

Nonce

33,556,055

Timestamp

11/26/2013, 4:23:16 AM

Confirmations

6,522,229

Merkle Root

15ff59833dfbb46ac592c3de8597f3cfc6f321f205dd913a51c9eee084a4c6a3
Transactions (1)
Coinbase15ff59833dfbb4…c9eee084a4c6a3
1 in β†’ 1 out10.0700 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.708 Γ— 10⁹⁴(95-digit number)
67084384159296465338…14536782023750390540
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
6.708 Γ— 10⁹⁴(95-digit number)
67084384159296465338…14536782023750390541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.341 Γ— 10⁹⁡(96-digit number)
13416876831859293067…29073564047500781081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.683 Γ— 10⁹⁡(96-digit number)
26833753663718586135…58147128095001562161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.366 Γ— 10⁹⁡(96-digit number)
53667507327437172270…16294256190003124321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.073 Γ— 10⁹⁢(97-digit number)
10733501465487434454…32588512380006248641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.146 Γ— 10⁹⁢(97-digit number)
21467002930974868908…65177024760012497281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.293 Γ— 10⁹⁢(97-digit number)
42934005861949737816…30354049520024994561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.586 Γ— 10⁹⁢(97-digit number)
85868011723899475633…60708099040049989121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.717 Γ— 10⁹⁷(98-digit number)
17173602344779895126…21416198080099978241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.434 Γ— 10⁹⁷(98-digit number)
34347204689559790253…42832396160199956481
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 274160

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 01bed5f6e0829642bb21c5fb700cd492bc80cfcf3fb33406235599366d0bd608

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 #274,160 on Chainz β†—
Circulating Supply:57,615,108 XPMΒ·at block #6,796,388 Β· updates every 60s
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