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Home/Chain Registry/Block #392,921

Block #392,921

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/6/2014, 6:36:24 PM Β· Difficulty 10.4438 Β· 6,431,678 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
baac0a71690d5e86d104864bd93496d4e4a6c3b09422503c7bfd679891d89e64
View on Chainz β†—

Height

#392,921

Difficulty

10.443777

Transactions

1

Size

205 B

Version

2

Bits

0a719b66

Nonce

153,242

Timestamp

2/6/2014, 6:36:24 PM

Confirmations

6,431,678

Merkle Root

39a157071ab1196c4e5141af919252782f1ab8580347bcd466e6ab6658d215b0
Transactions (1)
Coinbase39a157071ab119…e6ab6658d215b0
1 in β†’ 1 out9.1500 XPM116 B
AbwWkWZt…kawDhufa
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.

1.376 Γ— 10⁹³(94-digit number)
13763167027660867611…46187049714491392800
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
1.376 Γ— 10⁹³(94-digit number)
13763167027660867611…46187049714491392799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.752 Γ— 10⁹³(94-digit number)
27526334055321735223…92374099428982785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.505 Γ— 10⁹³(94-digit number)
55052668110643470447…84748198857965571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.101 Γ— 10⁹⁴(95-digit number)
11010533622128694089…69496397715931142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.202 Γ— 10⁹⁴(95-digit number)
22021067244257388178…38992795431862284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.404 Γ— 10⁹⁴(95-digit number)
44042134488514776357…77985590863724569599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.808 Γ— 10⁹⁴(95-digit number)
88084268977029552715…55971181727449139199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁡(96-digit number)
17616853795405910543…11942363454898278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.523 Γ— 10⁹⁡(96-digit number)
35233707590811821086…23884726909796556799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.046 Γ— 10⁹⁡(96-digit number)
70467415181623642172…47769453819593113599
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 392921

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 baac0a71690d5e86d104864bd93496d4e4a6c3b09422503c7bfd679891d89e64

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 #392,921 on Chainz β†—
Circulating Supply:57,840,861 XPMΒ·at block #6,824,598 Β· updates every 60s
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