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Home/Chain Registry/Block #669,849

Block #669,849

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2014, 4:39:46 AM Β· Difficulty 10.9640 Β· 6,162,142 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11ebe47ace111b5fb7da6c9c94bf229b43fbf819460da09cc04c98a30005cbf3
View on Chainz β†—

Height

#669,849

Difficulty

10.964049

Transactions

1

Size

207 B

Version

2

Bits

0af6cbe3

Nonce

1,223,997,946

Timestamp

8/9/2014, 4:39:46 AM

Confirmations

6,162,142

Merkle Root

13d611806c8a7faa1679a89174e481911a56b281cba0376c0b3fcfcedd6ffabc
Transactions (1)
Coinbase13d611806c8a7f…3fcfcedd6ffabc
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.498 Γ— 10⁹⁢(97-digit number)
54980615258726869619…46965698276122900480
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
5.498 Γ— 10⁹⁢(97-digit number)
54980615258726869619…46965698276122900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁷(98-digit number)
10996123051745373923…93931396552245800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.199 Γ— 10⁹⁷(98-digit number)
21992246103490747847…87862793104491601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.398 Γ— 10⁹⁷(98-digit number)
43984492206981495695…75725586208983203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.796 Γ— 10⁹⁷(98-digit number)
87968984413962991390…51451172417966407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.759 Γ— 10⁹⁸(99-digit number)
17593796882792598278…02902344835932815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.518 Γ— 10⁹⁸(99-digit number)
35187593765585196556…05804689671865630719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.037 Γ— 10⁹⁸(99-digit number)
70375187531170393112…11609379343731261439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.407 Γ— 10⁹⁹(100-digit number)
14075037506234078622…23218758687462522879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.815 Γ— 10⁹⁹(100-digit number)
28150075012468157245…46437517374925045759
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 669849

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 11ebe47ace111b5fb7da6c9c94bf229b43fbf819460da09cc04c98a30005cbf3

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 #669,849 on Chainz β†—
Circulating Supply:57,900,053 XPMΒ·at block #6,831,990 Β· updates every 60s
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