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Block #87,602

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2013, 12:52:41 AM Β· Difficulty 9.2718 Β· 6,708,922 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1f18430b7310fba9b39764eac81ebc1b660760ca7b8ed2d81c5faf925005bd1e
View on Chainz β†—

Height

#87,602

Difficulty

9.271752

Transactions

1

Size

201 B

Version

2

Bits

09459183

Nonce

38,648

Timestamp

7/29/2013, 12:52:41 AM

Confirmations

6,708,922

Merkle Root

6a6eb3756be2e96846170567a8193c97afdb40576be427ef53012449408d2e69
Transactions (1)
Coinbase6a6eb3756be2e9…012449408d2e69
1 in β†’ 1 out11.6200 XPM109 B
AcuJraLT…Y66BS47Q
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.

1.790 Γ— 10¹⁰⁰(101-digit number)
17905267951837034312…51107407083698285120
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
1.790 Γ— 10¹⁰⁰(101-digit number)
17905267951837034312…51107407083698285121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.581 Γ— 10¹⁰⁰(101-digit number)
35810535903674068625…02214814167396570241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.162 Γ— 10¹⁰⁰(101-digit number)
71621071807348137251…04429628334793140481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.432 Γ— 10¹⁰¹(102-digit number)
14324214361469627450…08859256669586280961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.864 Γ— 10¹⁰¹(102-digit number)
28648428722939254900…17718513339172561921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.729 Γ— 10¹⁰¹(102-digit number)
57296857445878509801…35437026678345123841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.145 Γ— 10¹⁰²(103-digit number)
11459371489175701960…70874053356690247681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.291 Γ— 10¹⁰²(103-digit number)
22918742978351403920…41748106713380495361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.583 Γ— 10¹⁰²(103-digit number)
45837485956702807841…83496213426760990721
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 87602

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 1f18430b7310fba9b39764eac81ebc1b660760ca7b8ed2d81c5faf925005bd1e

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 #87,602 on Chainz β†—
Circulating Supply:57,616,187 XPMΒ·at block #6,796,523 Β· updates every 60s
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