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Block #77,158

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2013, 7:47:38 AM Β· Difficulty 9.1501 Β· 6,719,163 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bd7fcc3077902d7c0fcfe297a0c6d8d4bf4d6b8e87758024d7b0ad59ff5cd83c
View on Chainz β†—

Height

#77,158

Difficulty

9.150137

Transactions

1

Size

198 B

Version

2

Bits

09266f65

Nonce

154

Timestamp

7/22/2013, 7:47:38 AM

Confirmations

6,719,163

Merkle Root

da38b18acd0c140de20b0c0cc4cb888fcfc0e6ba81338ad45c8f7a1d1fcfc3e9
Transactions (1)
Coinbaseda38b18acd0c14…8f7a1d1fcfc3e9
1 in β†’ 1 out11.9300 XPM110 B
AXWphP8T…4trwmtBM
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.

1.029 Γ— 10⁹⁰(91-digit number)
10299519187582301101…34252790482766246460
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
1.029 Γ— 10⁹⁰(91-digit number)
10299519187582301101…34252790482766246461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.059 Γ— 10⁹⁰(91-digit number)
20599038375164602203…68505580965532492921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.119 Γ— 10⁹⁰(91-digit number)
41198076750329204406…37011161931064985841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.239 Γ— 10⁹⁰(91-digit number)
82396153500658408813…74022323862129971681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.647 Γ— 10⁹¹(92-digit number)
16479230700131681762…48044647724259943361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.295 Γ— 10⁹¹(92-digit number)
32958461400263363525…96089295448519886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.591 Γ— 10⁹¹(92-digit number)
65916922800526727050…92178590897039773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.318 Γ— 10⁹²(93-digit number)
13183384560105345410…84357181794079546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.636 Γ— 10⁹²(93-digit number)
26366769120210690820…68714363588159093761
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 77158

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 bd7fcc3077902d7c0fcfe297a0c6d8d4bf4d6b8e87758024d7b0ad59ff5cd83c

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 #77,158 on Chainz β†—
Circulating Supply:57,614,557 XPMΒ·at block #6,796,320 Β· updates every 60s
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