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Home/Chain Registry/Block #2,923,291

Block #2,923,291

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2018, 12:03:27 AM Β· Difficulty 11.3635 Β· 3,916,698 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e98393c60d5c0dfad4471839684bfa253d7a013aa9241d1689c95f4374b60205
View on Chainz β†—

Difficulty

11.363487

Transactions

1

Size

201 B

Version

2

Bits

0b5d0d7f

Nonce

169,303,250

Timestamp

11/15/2018, 12:03:27 AM

Confirmations

3,916,698

Merkle Root

7a684a7602dc36886fa10be8b8f3b9b374f2c74b116827a6ac28a95bb6a9d7f8
Transactions (1)
Coinbase7a684a7602dc36…28a95bb6a9d7f8
1 in β†’ 1 out7.7300 XPM110 B
AbXwmGxD…4XXYP765
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.

7.312 Γ— 10⁹⁷(98-digit number)
73120672495978033059…53074826177874001920
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
7.312 Γ— 10⁹⁷(98-digit number)
73120672495978033059…53074826177874001919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.462 Γ— 10⁹⁸(99-digit number)
14624134499195606611…06149652355748003839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.924 Γ— 10⁹⁸(99-digit number)
29248268998391213223…12299304711496007679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.849 Γ— 10⁹⁸(99-digit number)
58496537996782426447…24598609422992015359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.169 Γ— 10⁹⁹(100-digit number)
11699307599356485289…49197218845984030719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.339 Γ— 10⁹⁹(100-digit number)
23398615198712970579…98394437691968061439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.679 Γ— 10⁹⁹(100-digit number)
46797230397425941158…96788875383936122879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.359 Γ— 10⁹⁹(100-digit number)
93594460794851882316…93577750767872245759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.871 Γ— 10¹⁰⁰(101-digit number)
18718892158970376463…87155501535744491519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.743 Γ— 10¹⁰⁰(101-digit number)
37437784317940752926…74311003071488983039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.487 Γ— 10¹⁰⁰(101-digit number)
74875568635881505853…48622006142977966079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2923291

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 e98393c60d5c0dfad4471839684bfa253d7a013aa9241d1689c95f4374b60205

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 #2,923,291 on Chainz β†—
Circulating Supply:57,964,221 XPMΒ·at block #6,839,988 Β· updates every 60s
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