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Block #207,717

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 2:41:08 PM Β· Difficulty 9.9037 Β· 6,598,797 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b900e119fdfcd7cb187ff01d2845fef86bfda2c272ea5fe5002dde4cda04ba1a
View on Chainz β†—

Height

#207,717

Difficulty

9.903671

Transactions

2

Size

702 B

Version

2

Bits

09e75701

Nonce

9,193

Timestamp

10/13/2013, 2:41:08 PM

Confirmations

6,598,797

Merkle Root

08ad7a001ea7c0f9fddbb14fd8c3ab395147dd24fef3cc90fcb35ce577cdfdc5
Transactions (2)
Coinbase0f588be7d57b2b…72711a2adfb925
1 in β†’ 1 out10.1900 XPM109 B
AcL5sy4e…eA5yf5zT
e32f81cc63db4c…d86cf08c876b74
4 in β†’ 1 out41.0300 XPM501 B
AKn6Weta…JQF2zmr9
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.

1.357 Γ— 10⁹⁹(100-digit number)
13575842499347210423…30786447121018508800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.357 Γ— 10⁹⁹(100-digit number)
13575842499347210423…30786447121018508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.715 Γ— 10⁹⁹(100-digit number)
27151684998694420846…61572894242037017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.430 Γ— 10⁹⁹(100-digit number)
54303369997388841693…23145788484074035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.086 Γ— 10¹⁰⁰(101-digit number)
10860673999477768338…46291576968148070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.172 Γ— 10¹⁰⁰(101-digit number)
21721347998955536677…92583153936296140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.344 Γ— 10¹⁰⁰(101-digit number)
43442695997911073355…85166307872592281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.688 Γ— 10¹⁰⁰(101-digit number)
86885391995822146710…70332615745184563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.737 Γ— 10¹⁰¹(102-digit number)
17377078399164429342…40665231490369126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.475 Γ— 10¹⁰¹(102-digit number)
34754156798328858684…81330462980738252799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 207717

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 b900e119fdfcd7cb187ff01d2845fef86bfda2c272ea5fe5002dde4cda04ba1a

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 #207,717 on Chainz β†—
Circulating Supply:57,696,210 XPMΒ·at block #6,806,513 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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