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Block #122,395

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2013, 11:12:31 AM Β· Difficulty 9.7551 Β· 6,693,775 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f1b2a2050cd877915b2d557b3cb49409bf94ac5fd962ea4b477727070cd231f
View on Chainz β†—

Height

#122,395

Difficulty

9.755148

Transactions

1

Size

200 B

Version

2

Bits

09c15161

Nonce

208,297

Timestamp

8/18/2013, 11:12:31 AM

Confirmations

6,693,775

Merkle Root

c0b99c9b1b675f4320d9b350dd7de4acf017d0220691731b825198f83395e722
Transactions (1)
Coinbasec0b99c9b1b675f…5198f83395e722
1 in β†’ 1 out10.4900 XPM109 B
AKaGDwVV…h5Bk5GFu
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.

1.001 Γ— 10⁹⁸(99-digit number)
10013122320139325638…07850840826623054420
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
1.001 Γ— 10⁹⁸(99-digit number)
10013122320139325638…07850840826623054421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.002 Γ— 10⁹⁸(99-digit number)
20026244640278651277…15701681653246108841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.005 Γ— 10⁹⁸(99-digit number)
40052489280557302554…31403363306492217681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.010 Γ— 10⁹⁸(99-digit number)
80104978561114605108…62806726612984435361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.602 Γ— 10⁹⁹(100-digit number)
16020995712222921021…25613453225968870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.204 Γ— 10⁹⁹(100-digit number)
32041991424445842043…51226906451937741441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.408 Γ— 10⁹⁹(100-digit number)
64083982848891684086…02453812903875482881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.281 Γ— 10¹⁰⁰(101-digit number)
12816796569778336817…04907625807750965761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.563 Γ— 10¹⁰⁰(101-digit number)
25633593139556673634…09815251615501931521
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 122395

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 6f1b2a2050cd877915b2d557b3cb49409bf94ac5fd962ea4b477727070cd231f

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 #122,395 on Chainz β†—
Circulating Supply:57,773,483 XPMΒ·at block #6,816,169 Β· updates every 60s
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