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Home/Chain Registry/Block #849,197

Block #849,197

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/11/2014, 3:53:18 PM Β· Difficulty 10.9713 Β· 5,984,580 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
27661d7cf02df7fa26a55cbeee5970364378bae576b225c84f0a9ff0d82c8590
View on Chainz β†—

Height

#849,197

Difficulty

10.971297

Transactions

3

Size

591 B

Version

2

Bits

0af8a6e6

Nonce

1,267,838,212

Timestamp

12/11/2014, 3:53:18 PM

Confirmations

5,984,580

Merkle Root

7d3eea2fd7cdbe0eb78a7c8a44aa38fb26d9f767f61997b9ed12989836ef1a65
Transactions (3)
Coinbasec20eb1cf0a3db4…f02df5a7c71891
1 in β†’ 1 out8.3215 XPM116 B
ANSXnLY2…Sd25TjkD
39123aa33e70ea…7d7d72c980ba38
1 in β†’ 1 out0.0103 XPM192 B
Aa4ycsvD…Usx91fZC
99ef43f6ed7bee…e7c2f2117d0567
1 in β†’ 1 out0.0102 XPM193 B
AQje2Jag…7fm5zupb
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.

5.090 Γ— 10⁹⁡(96-digit number)
50903773422520401108…01868836932886055700
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
5.090 Γ— 10⁹⁡(96-digit number)
50903773422520401108…01868836932886055699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.018 Γ— 10⁹⁢(97-digit number)
10180754684504080221…03737673865772111399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.036 Γ— 10⁹⁢(97-digit number)
20361509369008160443…07475347731544222799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.072 Γ— 10⁹⁢(97-digit number)
40723018738016320886…14950695463088445599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.144 Γ— 10⁹⁢(97-digit number)
81446037476032641773…29901390926176891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.628 Γ— 10⁹⁷(98-digit number)
16289207495206528354…59802781852353782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.257 Γ— 10⁹⁷(98-digit number)
32578414990413056709…19605563704707564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.515 Γ— 10⁹⁷(98-digit number)
65156829980826113418…39211127409415129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁸(99-digit number)
13031365996165222683…78422254818830259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.606 Γ— 10⁹⁸(99-digit number)
26062731992330445367…56844509637660518399
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 849197

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 27661d7cf02df7fa26a55cbeee5970364378bae576b225c84f0a9ff0d82c8590

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 #849,197 on Chainz β†—
Circulating Supply:57,914,434 XPMΒ·at block #6,833,776 Β· updates every 60s
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