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Block #123,051

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2013, 8:17:24 PM Β· Difficulty 9.7605 Β· 6,674,801 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5948d3c0f0e2439771924631d17dc39f876a20c5f1efaa7efe838f688a68b0a6
View on Chainz β†—

Height

#123,051

Difficulty

9.760509

Transactions

1

Size

201 B

Version

2

Bits

09c2b0bd

Nonce

152,195

Timestamp

8/18/2013, 8:17:24 PM

Confirmations

6,674,801

Merkle Root

b7c66b9ee02efeea0f9e0ac47bd17cefdbf96532a50c37c71b38600b54b022b1
Transactions (1)
Coinbaseb7c66b9ee02efe…38600b54b022b1
1 in β†’ 1 out10.4800 XPM110 B
ATC9ronQ…PtcbLicH
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.

6.243 Γ— 10⁹⁷(98-digit number)
62430223228297589919…87877920874964340800
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
6.243 Γ— 10⁹⁷(98-digit number)
62430223228297589919…87877920874964340801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.248 Γ— 10⁹⁸(99-digit number)
12486044645659517983…75755841749928681601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.497 Γ— 10⁹⁸(99-digit number)
24972089291319035967…51511683499857363201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.994 Γ— 10⁹⁸(99-digit number)
49944178582638071935…03023366999714726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.988 Γ— 10⁹⁸(99-digit number)
99888357165276143871…06046733999429452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.997 Γ— 10⁹⁹(100-digit number)
19977671433055228774…12093467998858905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.995 Γ— 10⁹⁹(100-digit number)
39955342866110457548…24186935997717811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.991 Γ— 10⁹⁹(100-digit number)
79910685732220915097…48373871995435622401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.598 Γ— 10¹⁰⁰(101-digit number)
15982137146444183019…96747743990871244801
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 123051

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 5948d3c0f0e2439771924631d17dc39f876a20c5f1efaa7efe838f688a68b0a6

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 #123,051 on Chainz β†—
Circulating Supply:57,626,800 XPMΒ·at block #6,797,851 Β· updates every 60s
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