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Home/Chain Registry/Block #669,848

Block #669,848

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2014, 4:39:49 AM Β· Difficulty 10.9640 Β· 6,163,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57cf08b003be7f01b94f44b384d39208e83f87f1c1eb3e0e5d32cf464df29a4e
View on Chainz β†—

Height

#669,848

Difficulty

10.964045

Transactions

1

Size

207 B

Version

2

Bits

0af6cba5

Nonce

172,581,053

Timestamp

8/9/2014, 4:39:49 AM

Confirmations

6,163,017

Merkle Root

8a2cbf78410b31607bc7b5d2952ff20470c3499265a7d6db07c6930a0a69cb1a
Transactions (1)
Coinbase8a2cbf78410b31…c6930a0a69cb1a
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.

4.298 Γ— 10⁹⁷(98-digit number)
42980450049470736465…75019722440336834560
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.298 Γ— 10⁹⁷(98-digit number)
42980450049470736465…75019722440336834561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.596 Γ— 10⁹⁷(98-digit number)
85960900098941472931…50039444880673669121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.719 Γ— 10⁹⁸(99-digit number)
17192180019788294586…00078889761347338241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.438 Γ— 10⁹⁸(99-digit number)
34384360039576589172…00157779522694676481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.876 Γ— 10⁹⁸(99-digit number)
68768720079153178345…00315559045389352961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.375 Γ— 10⁹⁹(100-digit number)
13753744015830635669…00631118090778705921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.750 Γ— 10⁹⁹(100-digit number)
27507488031661271338…01262236181557411841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.501 Γ— 10⁹⁹(100-digit number)
55014976063322542676…02524472363114823681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.100 Γ— 10¹⁰⁰(101-digit number)
11002995212664508535…05048944726229647361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.200 Γ— 10¹⁰⁰(101-digit number)
22005990425329017070…10097889452459294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.401 Γ— 10¹⁰⁰(101-digit number)
44011980850658034140…20195778904918589441
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 669848

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 57cf08b003be7f01b94f44b384d39208e83f87f1c1eb3e0e5d32cf464df29a4e

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 #669,848 on Chainz β†—
Circulating Supply:57,907,087 XPMΒ·at block #6,832,864 Β· updates every 60s
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