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Block #205,069

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/11/2013, 10:14:41 PM Β· Difficulty 9.8992 Β· 6,606,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86ff99e773e492cf3545471ce0bf8642e7dd52a2a8873a5a0c21c7b2b10e391f
View on Chainz β†—

Height

#205,069

Difficulty

9.899172

Transactions

1

Size

201 B

Version

2

Bits

09e63029

Nonce

21,915

Timestamp

10/11/2013, 10:14:41 PM

Confirmations

6,606,710

Merkle Root

f896b9e6b6cefd42116f982ed33da6d9b9fae746a04e1917df69f59a4ab6d877
Transactions (1)
Coinbasef896b9e6b6cefd…69f59a4ab6d877
1 in β†’ 1 out10.1900 XPM109 B
AVQtj9sz…4P34aCDq
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.

2.810 Γ— 10⁹⁸(99-digit number)
28102214465907120344…47944638147841026640
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
2.810 Γ— 10⁹⁸(99-digit number)
28102214465907120344…47944638147841026639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.620 Γ— 10⁹⁸(99-digit number)
56204428931814240688…95889276295682053279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.124 Γ— 10⁹⁹(100-digit number)
11240885786362848137…91778552591364106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.248 Γ— 10⁹⁹(100-digit number)
22481771572725696275…83557105182728213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.496 Γ— 10⁹⁹(100-digit number)
44963543145451392550…67114210365456426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.992 Γ— 10⁹⁹(100-digit number)
89927086290902785101…34228420730912852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.798 Γ— 10¹⁰⁰(101-digit number)
17985417258180557020…68456841461825704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.597 Γ— 10¹⁰⁰(101-digit number)
35970834516361114040…36913682923651409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.194 Γ— 10¹⁰⁰(101-digit number)
71941669032722228081…73827365847302819839
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 205069

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 86ff99e773e492cf3545471ce0bf8642e7dd52a2a8873a5a0c21c7b2b10e391f

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 #205,069 on Chainz β†—
Circulating Supply:57,738,343 XPMΒ·at block #6,811,778 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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