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Home/Chain Registry/Block #2,669,613

Block #2,669,613

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2018, 8:12:20 AM Β· Difficulty 11.6797 Β· 4,169,765 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
92dbf6ff2100857f8291400a8b33dcd2b8e6bdabca84b3e85493fe01255ee0f5
View on Chainz β†—

Difficulty

11.679726

Transactions

1

Size

200 B

Version

2

Bits

0bae0284

Nonce

262,907,670

Timestamp

5/20/2018, 8:12:20 AM

Confirmations

4,169,765

Merkle Root

5cb75f8b3fb563fd84f8753ba0096a56126b6df8e422c7da698e9287263ca0e7
Transactions (1)
Coinbase5cb75f8b3fb563…8e9287263ca0e7
1 in β†’ 1 out7.3200 XPM110 B
AaJ84d36…skcyKrD4
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.

2.598 Γ— 10⁹⁡(96-digit number)
25982393239650018751…61017005608376153600
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
2.598 Γ— 10⁹⁡(96-digit number)
25982393239650018751…61017005608376153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.196 Γ— 10⁹⁡(96-digit number)
51964786479300037502…22034011216752307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.039 Γ— 10⁹⁢(97-digit number)
10392957295860007500…44068022433504614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.078 Γ— 10⁹⁢(97-digit number)
20785914591720015000…88136044867009228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.157 Γ— 10⁹⁢(97-digit number)
41571829183440030001…76272089734018457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.314 Γ— 10⁹⁢(97-digit number)
83143658366880060003…52544179468036915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.662 Γ— 10⁹⁷(98-digit number)
16628731673376012000…05088358936073830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.325 Γ— 10⁹⁷(98-digit number)
33257463346752024001…10176717872147660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.651 Γ— 10⁹⁷(98-digit number)
66514926693504048003…20353435744295321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.330 Γ— 10⁹⁸(99-digit number)
13302985338700809600…40706871488590643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.660 Γ— 10⁹⁸(99-digit number)
26605970677401619201…81413742977181286401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2669613

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 92dbf6ff2100857f8291400a8b33dcd2b8e6bdabca84b3e85493fe01255ee0f5

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 #2,669,613 on Chainz β†—
Circulating Supply:57,959,307 XPMΒ·at block #6,839,377 Β· updates every 60s
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