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Home/Chain Registry/Block #669,111

Block #669,111

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2014, 4:40:38 PM Β· Difficulty 10.9639 Β· 6,131,622 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
12889947c440226dbc417b54b18d4a3b63cbf3b63d97d12fb449d0bb0bf4a1bc
View on Chainz β†—

Height

#669,111

Difficulty

10.963894

Transactions

2

Size

581 B

Version

2

Bits

0af6c1c4

Nonce

411,038,266

Timestamp

8/8/2014, 4:40:38 PM

Confirmations

6,131,622

Merkle Root

8b5806bcbbc5ffeb626a8943ae3b367c861656f05463781a275e80e546b7a903
Transactions (2)
Coinbase48b56359ea839c…d67a4245754dca
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
680b238e86fa75…00a8aa7fbf35d0
2 in β†’ 2 out1.9060 XPM374 B
AGWMp78N…2xUjW2r4AKxgMkSn…tVzwz1ph
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.

1.417 Γ— 10⁹⁷(98-digit number)
14176480819123549308…52378154147102883840
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
1.417 Γ— 10⁹⁷(98-digit number)
14176480819123549308…52378154147102883839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.835 Γ— 10⁹⁷(98-digit number)
28352961638247098616…04756308294205767679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.670 Γ— 10⁹⁷(98-digit number)
56705923276494197232…09512616588411535359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.134 Γ— 10⁹⁸(99-digit number)
11341184655298839446…19025233176823070719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.268 Γ— 10⁹⁸(99-digit number)
22682369310597678893…38050466353646141439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.536 Γ— 10⁹⁸(99-digit number)
45364738621195357786…76100932707292282879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.072 Γ— 10⁹⁸(99-digit number)
90729477242390715572…52201865414584565759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.814 Γ— 10⁹⁹(100-digit number)
18145895448478143114…04403730829169131519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.629 Γ— 10⁹⁹(100-digit number)
36291790896956286229…08807461658338263039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.258 Γ— 10⁹⁹(100-digit number)
72583581793912572458…17614923316676526079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.451 Γ— 10¹⁰⁰(101-digit number)
14516716358782514491…35229846633353052159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 669111

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 12889947c440226dbc417b54b18d4a3b63cbf3b63d97d12fb449d0bb0bf4a1bc

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 #669,111 on Chainz β†—
Circulating Supply:57,649,934 XPMΒ·at block #6,800,732 Β· updates every 60s
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