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Block #157,489

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 4:08:25 PM Β· Difficulty 9.8692 Β· 6,659,403 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
78954301cb5abfedd68632905a17ec0b46ef71e0b613fb0f311905d0b404fe7e
View on Chainz β†—

Height

#157,489

Difficulty

9.869167

Transactions

1

Size

199 B

Version

2

Bits

09de81c0

Nonce

76,073

Timestamp

9/9/2013, 4:08:25 PM

Confirmations

6,659,403

Merkle Root

06a427cf301420e6bb73238bd61cbcbcd7d0e579fd0b5f384ecba689b3eb8d17
Transactions (1)
Coinbase06a427cf301420…cba689b3eb8d17
1 in β†’ 1 out10.2500 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.

1.317 Γ— 10⁹⁡(96-digit number)
13178555153353315058…68381108217434871040
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
1.317 Γ— 10⁹⁡(96-digit number)
13178555153353315058…68381108217434871041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.635 Γ— 10⁹⁡(96-digit number)
26357110306706630116…36762216434869742081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.271 Γ— 10⁹⁡(96-digit number)
52714220613413260233…73524432869739484161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.054 Γ— 10⁹⁢(97-digit number)
10542844122682652046…47048865739478968321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.108 Γ— 10⁹⁢(97-digit number)
21085688245365304093…94097731478957936641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.217 Γ— 10⁹⁢(97-digit number)
42171376490730608186…88195462957915873281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.434 Γ— 10⁹⁢(97-digit number)
84342752981461216373…76390925915831746561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.686 Γ— 10⁹⁷(98-digit number)
16868550596292243274…52781851831663493121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.373 Γ— 10⁹⁷(98-digit number)
33737101192584486549…05563703663326986241
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 157489

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 78954301cb5abfedd68632905a17ec0b46ef71e0b613fb0f311905d0b404fe7e

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 #157,489 on Chainz β†—
Circulating Supply:57,779,177 XPMΒ·at block #6,816,891 Β· updates every 60s
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