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Block #116,912

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/14/2013, 5:21:40 PM Β· Difficulty 9.7502 Β· 6,710,007 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
17f27e0726b22cd4d55a4c044d8bc9b981f7056b31c9ef26e6d6ef09f21026a4
View on Chainz β†—

Height

#116,912

Difficulty

9.750235

Transactions

1

Size

200 B

Version

2

Bits

09c00f60

Nonce

31,511

Timestamp

8/14/2013, 5:21:40 PM

Confirmations

6,710,007

Merkle Root

ae7509822ad109e6370e754e58da6f2856a839a66bf34a93fe6cbd34b08ab974
Transactions (1)
Coinbaseae7509822ad109…6cbd34b08ab974
1 in β†’ 1 out10.5000 XPM109 B
ATLxyWN9…uyU1wmmy
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.

4.186 Γ— 10⁹⁢(97-digit number)
41860329226217381110…82175897369389178780
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
4.186 Γ— 10⁹⁢(97-digit number)
41860329226217381110…82175897369389178779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.372 Γ— 10⁹⁢(97-digit number)
83720658452434762220…64351794738778357559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁷(98-digit number)
16744131690486952444…28703589477556715119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁷(98-digit number)
33488263380973904888…57407178955113430239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.697 Γ— 10⁹⁷(98-digit number)
66976526761947809776…14814357910226860479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁸(99-digit number)
13395305352389561955…29628715820453720959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.679 Γ— 10⁹⁸(99-digit number)
26790610704779123910…59257431640907441919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.358 Γ— 10⁹⁸(99-digit number)
53581221409558247821…18514863281814883839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁹(100-digit number)
10716244281911649564…37029726563629767679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁹(100-digit number)
21432488563823299128…74059453127259535359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 116912

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 17f27e0726b22cd4d55a4c044d8bc9b981f7056b31c9ef26e6d6ef09f21026a4

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 #116,912 on Chainz β†—
Circulating Supply:57,859,522 XPMΒ·at block #6,826,918 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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