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Home/Chain Registry/Block #162,008

Block #162,008

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 12:47:59 AM Β· Difficulty 9.8608 Β· 6,665,361 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64c78ea43644b82c26ab16d45f0768bc8fa8abbff7ecafa237b5e73402eb5ef5
View on Chainz β†—

Height

#162,008

Difficulty

9.860838

Transactions

1

Size

199 B

Version

2

Bits

09dc5fda

Nonce

286,108

Timestamp

9/13/2013, 12:47:59 AM

Confirmations

6,665,361

Merkle Root

77fb577230a4084686887acc83dacbb121c2f2bf87609226f34421c720ede9c3
Transactions (1)
Coinbase77fb577230a408…4421c720ede9c3
1 in β†’ 1 out10.2700 XPM109 B
Abz81iaE…wwQqTw3G
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.

2.497 Γ— 10⁹⁡(96-digit number)
24972634758551415516…32644025840582680420
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
2.497 Γ— 10⁹⁡(96-digit number)
24972634758551415516…32644025840582680421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.994 Γ— 10⁹⁡(96-digit number)
49945269517102831032…65288051681165360841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.989 Γ— 10⁹⁡(96-digit number)
99890539034205662064…30576103362330721681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.997 Γ— 10⁹⁢(97-digit number)
19978107806841132412…61152206724661443361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.995 Γ— 10⁹⁢(97-digit number)
39956215613682264825…22304413449322886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.991 Γ— 10⁹⁢(97-digit number)
79912431227364529651…44608826898645773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.598 Γ— 10⁹⁷(98-digit number)
15982486245472905930…89217653797291546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.196 Γ— 10⁹⁷(98-digit number)
31964972490945811860…78435307594583093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.392 Γ— 10⁹⁷(98-digit number)
63929944981891623721…56870615189166187521
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 162008

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 64c78ea43644b82c26ab16d45f0768bc8fa8abbff7ecafa237b5e73402eb5ef5

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 #162,008 on Chainz β†—
Circulating Supply:57,863,053 XPMΒ·at block #6,827,368 Β· updates every 60s
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