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Block #123,327

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/19/2013, 12:06:23 AM Β· Difficulty 9.7627 Β· 6,690,517 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c985b813b4e6d81ff6eaf5f653cdfc06b9c0457fb20861df0c5ff540f570489d
View on Chainz β†—

Height

#123,327

Difficulty

9.762717

Transactions

1

Size

199 B

Version

2

Bits

09c34168

Nonce

13,090

Timestamp

8/19/2013, 12:06:23 AM

Confirmations

6,690,517

Merkle Root

8beff14df5b64612b3da4cbf9961f3b37c248239cfb57afe093f593b118da0eb
Transactions (1)
Coinbase8beff14df5b646…3f593b118da0eb
1 in β†’ 1 out10.4800 XPM109 B
AVJaZtXC…gGZDZ3Yk
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.

7.850 Γ— 10⁹⁴(95-digit number)
78503390347126635357…22663325436517437640
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
7.850 Γ— 10⁹⁴(95-digit number)
78503390347126635357…22663325436517437641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.570 Γ— 10⁹⁡(96-digit number)
15700678069425327071…45326650873034875281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.140 Γ— 10⁹⁡(96-digit number)
31401356138850654143…90653301746069750561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.280 Γ— 10⁹⁡(96-digit number)
62802712277701308286…81306603492139501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.256 Γ— 10⁹⁢(97-digit number)
12560542455540261657…62613206984279002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.512 Γ— 10⁹⁢(97-digit number)
25121084911080523314…25226413968558004481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.024 Γ— 10⁹⁢(97-digit number)
50242169822161046629…50452827937116008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.004 Γ— 10⁹⁷(98-digit number)
10048433964432209325…00905655874232017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.009 Γ— 10⁹⁷(98-digit number)
20096867928864418651…01811311748464035841
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 123327

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 c985b813b4e6d81ff6eaf5f653cdfc06b9c0457fb20861df0c5ff540f570489d

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 #123,327 on Chainz β†—
Circulating Supply:57,754,821 XPMΒ·at block #6,813,843 Β· updates every 60s
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