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Block #35,692

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 8:26:49 AM Β· Difficulty 7.9947 Β· 6,768,220 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
80700823cf62e6fc2916d157906953fb30589c71cc845a28980516d1695694d0
View on Chainz β†—

Height

#35,692

Difficulty

7.994676

Transactions

1

Size

203 B

Version

2

Bits

07fea30e

Nonce

89

Timestamp

7/14/2013, 8:26:49 AM

Confirmations

6,768,220

Merkle Root

291937472494863e3d385962c7777cd75ac89874fa28b3002b2b060ef965ab3e
Transactions (1)
Coinbase29193747249486…2b060ef965ab3e
1 in β†’ 1 out15.6300 XPM109 B
AKsLKPc8…zkBgUqcr
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.

2.632 Γ— 10¹⁰⁡(106-digit number)
26328512590615393206…36152818186681509100
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
2.632 Γ— 10¹⁰⁡(106-digit number)
26328512590615393206…36152818186681509101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.265 Γ— 10¹⁰⁡(106-digit number)
52657025181230786413…72305636373363018201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.053 Γ— 10¹⁰⁢(107-digit number)
10531405036246157282…44611272746726036401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.106 Γ— 10¹⁰⁢(107-digit number)
21062810072492314565…89222545493452072801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.212 Γ— 10¹⁰⁢(107-digit number)
42125620144984629130…78445090986904145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.425 Γ— 10¹⁰⁢(107-digit number)
84251240289969258261…56890181973808291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.685 Γ— 10¹⁰⁷(108-digit number)
16850248057993851652…13780363947616582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.370 Γ— 10¹⁰⁷(108-digit number)
33700496115987703304…27560727895233164801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.740 Γ— 10¹⁰⁷(108-digit number)
67400992231975406609…55121455790466329601
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 35692

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 80700823cf62e6fc2916d157906953fb30589c71cc845a28980516d1695694d0

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 #35,692 on Chainz β†—
Circulating Supply:57,675,343 XPMΒ·at block #6,803,911 Β· updates every 60s
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