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Home/Chain Registry/Block #849,196

Block #849,196

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/11/2014, 3:51:50 PM Β· Difficulty 10.9713 Β· 5,984,296 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd0053b93850f7495587f221168631b645e4eea7a031777564e21e066c2681d1
View on Chainz β†—

Height

#849,196

Difficulty

10.971293

Transactions

1

Size

207 B

Version

2

Bits

0af8a6ac

Nonce

977,765,296

Timestamp

12/11/2014, 3:51:50 PM

Confirmations

5,984,296

Merkle Root

8eb3baabb10e180d720deed4dcfd8904a2e5ef7ddd57497a7050076aca6892ed
Transactions (1)
Coinbase8eb3baabb10e18…50076aca6892ed
1 in β†’ 1 out8.2900 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.

3.785 Γ— 10⁹⁷(98-digit number)
37857014727284205318…97748229315186780160
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
3.785 Γ— 10⁹⁷(98-digit number)
37857014727284205318…97748229315186780161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.571 Γ— 10⁹⁷(98-digit number)
75714029454568410636…95496458630373560321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.514 Γ— 10⁹⁸(99-digit number)
15142805890913682127…90992917260747120641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.028 Γ— 10⁹⁸(99-digit number)
30285611781827364254…81985834521494241281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.057 Γ— 10⁹⁸(99-digit number)
60571223563654728508…63971669042988482561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.211 Γ— 10⁹⁹(100-digit number)
12114244712730945701…27943338085976965121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.422 Γ— 10⁹⁹(100-digit number)
24228489425461891403…55886676171953930241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.845 Γ— 10⁹⁹(100-digit number)
48456978850923782807…11773352343907860481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.691 Γ— 10⁹⁹(100-digit number)
96913957701847565614…23546704687815720961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.938 Γ— 10¹⁰⁰(101-digit number)
19382791540369513122…47093409375631441921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.876 Γ— 10¹⁰⁰(101-digit number)
38765583080739026245…94186818751262883841
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 849196

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 dd0053b93850f7495587f221168631b645e4eea7a031777564e21e066c2681d1

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 #849,196 on Chainz β†—
Circulating Supply:57,912,142 XPMΒ·at block #6,833,491 Β· updates every 60s
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