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Home/Chain Registry/Block #1,692,744

Block #1,692,744

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2016, 2:44:21 PM Β· Difficulty 10.6812 Β· 5,138,059 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b6dd9da1c1f54c97d832a6fbb847fa06f3bf8a327e8e1f4d0043ab8758128d2c
View on Chainz β†—

Difficulty

10.681226

Transactions

1

Size

243 B

Version

2

Bits

0aae64d8

Nonce

830,478,348

Timestamp

7/28/2016, 2:44:21 PM

Confirmations

5,138,059

Merkle Root

7ae3c05c28e7fb72f467a21e8eaeebbc1c6d85ec7a67747353009b75d13e2ad2
Transactions (1)
Coinbase7ae3c05c28e7fb…009b75d13e2ad2
1 in β†’ 2 out8.7500 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

5.489 Γ— 10⁹⁢(97-digit number)
54898865760256368763…44485685014611681280
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
5.489 Γ— 10⁹⁢(97-digit number)
54898865760256368763…44485685014611681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁷(98-digit number)
10979773152051273752…88971370029223362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.195 Γ— 10⁹⁷(98-digit number)
21959546304102547505…77942740058446725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.391 Γ— 10⁹⁷(98-digit number)
43919092608205095011…55885480116893450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.783 Γ— 10⁹⁷(98-digit number)
87838185216410190022…11770960233786900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.756 Γ— 10⁹⁸(99-digit number)
17567637043282038004…23541920467573800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.513 Γ— 10⁹⁸(99-digit number)
35135274086564076008…47083840935147601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.027 Γ— 10⁹⁸(99-digit number)
70270548173128152017…94167681870295203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.405 Γ— 10⁹⁹(100-digit number)
14054109634625630403…88335363740590407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.810 Γ— 10⁹⁹(100-digit number)
28108219269251260807…76670727481180815359
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 1692744

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 b6dd9da1c1f54c97d832a6fbb847fa06f3bf8a327e8e1f4d0043ab8758128d2c

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 #1,692,744 on Chainz β†—
Circulating Supply:57,890,556 XPMΒ·at block #6,830,802 Β· updates every 60s
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