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Block #100,670

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2013, 6:51:04 AM Β· Difficulty 9.4348 Β· 6,715,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67886f6c2ab55a384aa3b1b50454f96835c1ba5ebcf56cede0308ddc9ef17aa4
View on Chainz β†—

Height

#100,670

Difficulty

9.434809

Transactions

1

Size

201 B

Version

2

Bits

096f4f9d

Nonce

5,789

Timestamp

8/6/2013, 6:51:04 AM

Confirmations

6,715,642

Merkle Root

8bc6b4d3393a19ca0e59120791a14ebd3a292bc0a9dec84469c7ed5e7dfe8b69
Transactions (1)
Coinbase8bc6b4d3393a19…c7ed5e7dfe8b69
1 in β†’ 1 out11.2200 XPM109 B
Ac61dvZd…bFLso2oz
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.

2.940 Γ— 10⁹⁸(99-digit number)
29404472058626942056…10690812425638258080
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
2.940 Γ— 10⁹⁸(99-digit number)
29404472058626942056…10690812425638258081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.880 Γ— 10⁹⁸(99-digit number)
58808944117253884112…21381624851276516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.176 Γ— 10⁹⁹(100-digit number)
11761788823450776822…42763249702553032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.352 Γ— 10⁹⁹(100-digit number)
23523577646901553645…85526499405106064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.704 Γ— 10⁹⁹(100-digit number)
47047155293803107290…71052998810212129281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.409 Γ— 10⁹⁹(100-digit number)
94094310587606214580…42105997620424258561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.881 Γ— 10¹⁰⁰(101-digit number)
18818862117521242916…84211995240848517121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.763 Γ— 10¹⁰⁰(101-digit number)
37637724235042485832…68423990481697034241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.527 Γ— 10¹⁰⁰(101-digit number)
75275448470084971664…36847980963394068481
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 100670

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 67886f6c2ab55a384aa3b1b50454f96835c1ba5ebcf56cede0308ddc9ef17aa4

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 #100,670 on Chainz β†—
Circulating Supply:57,774,615 XPMΒ·at block #6,816,311 Β· updates every 60s
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