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Home/Chain Registry/Block #1,685,364

Block #1,685,364

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2016, 12:19:50 AM Β· Difficulty 10.7213 Β· 5,157,808 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfc9a248ae0b795d4a7bd71efc93574f170ca86ddf851732a41b2e206150f4aa
View on Chainz β†—

Difficulty

10.721297

Transactions

1

Size

199 B

Version

2

Bits

0ab8a6ee

Nonce

1,968,944,782

Timestamp

7/23/2016, 12:19:50 AM

Confirmations

5,157,808

Merkle Root

bf3f5875c2117371744b8176c6897ff7c03ee434f313b3fcab30c799bc4796bb
Transactions (1)
Coinbasebf3f5875c21173…30c799bc4796bb
1 in β†’ 1 out8.6900 XPM109 B
AK3UzTKh…PP6WjtZ6
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.

1.589 Γ— 10⁹⁴(95-digit number)
15892500549657212692…56404051874664285040
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
1.589 Γ— 10⁹⁴(95-digit number)
15892500549657212692…56404051874664285039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.178 Γ— 10⁹⁴(95-digit number)
31785001099314425385…12808103749328570079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.357 Γ— 10⁹⁴(95-digit number)
63570002198628850770…25616207498657140159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁡(96-digit number)
12714000439725770154…51232414997314280319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.542 Γ— 10⁹⁡(96-digit number)
25428000879451540308…02464829994628560639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.085 Γ— 10⁹⁡(96-digit number)
50856001758903080616…04929659989257121279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.017 Γ— 10⁹⁢(97-digit number)
10171200351780616123…09859319978514242559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.034 Γ— 10⁹⁢(97-digit number)
20342400703561232246…19718639957028485119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.068 Γ— 10⁹⁢(97-digit number)
40684801407122464492…39437279914056970239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.136 Γ— 10⁹⁢(97-digit number)
81369602814244928985…78874559828113940479
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 1685364

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 cfc9a248ae0b795d4a7bd71efc93574f170ca86ddf851732a41b2e206150f4aa

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 #1,685,364 on Chainz β†—
Circulating Supply:57,989,742 XPMΒ·at block #6,843,171 Β· updates every 60s
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