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Home/Chain Registry/Block #1,885,097

Block #1,885,097

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/8/2016, 9:30:36 PM Β· Difficulty 10.7149 Β· 4,946,244 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f1ff134fc07a8434ac4f2ad18e0a5473590f35ab429acfac43c54d979a1653e7
View on Chainz β†—

Difficulty

10.714945

Transactions

1

Size

200 B

Version

2

Bits

0ab7069d

Nonce

550,892,746

Timestamp

12/8/2016, 9:30:36 PM

Confirmations

4,946,244

Merkle Root

dbac5c74d5cb2828a0f2c00cec9439ee6cca79de6a8a1fd016f089fc073a2136
Transactions (1)
Coinbasedbac5c74d5cb28…f089fc073a2136
1 in β†’ 1 out8.7000 XPM110 B
AY6CdkpZ…FC8m1bRE
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.

6.631 Γ— 10⁹⁴(95-digit number)
66318777797001935089…84867415732837061120
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
6.631 Γ— 10⁹⁴(95-digit number)
66318777797001935089…84867415732837061119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.326 Γ— 10⁹⁡(96-digit number)
13263755559400387017…69734831465674122239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.652 Γ— 10⁹⁡(96-digit number)
26527511118800774035…39469662931348244479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.305 Γ— 10⁹⁡(96-digit number)
53055022237601548071…78939325862696488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.061 Γ— 10⁹⁢(97-digit number)
10611004447520309614…57878651725392977919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.122 Γ— 10⁹⁢(97-digit number)
21222008895040619228…15757303450785955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.244 Γ— 10⁹⁢(97-digit number)
42444017790081238457…31514606901571911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.488 Γ— 10⁹⁢(97-digit number)
84888035580162476914…63029213803143823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.697 Γ— 10⁹⁷(98-digit number)
16977607116032495382…26058427606287646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.395 Γ— 10⁹⁷(98-digit number)
33955214232064990765…52116855212575293439
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 1885097

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 f1ff134fc07a8434ac4f2ad18e0a5473590f35ab429acfac43c54d979a1653e7

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 #1,885,097 on Chainz β†—
Circulating Supply:57,894,882 XPMΒ·at block #6,831,340 Β· updates every 60s
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