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Home/Chain Registry/Block #3,008,055

Block #3,008,055

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2019, 4:02:06 PM Β· Difficulty 11.2036 Β· 3,835,575 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e9289c2d9d75de83560acfefaa33da21d2bb8939e51a5665b98ff20b8b3a9bd5
View on Chainz β†—

Difficulty

11.203628

Transactions

1

Size

201 B

Version

2

Bits

0b3420fe

Nonce

467,176,522

Timestamp

1/13/2019, 4:02:06 PM

Confirmations

3,835,575

Merkle Root

18ecdd6794b235c31de2c4a6a3476af26a04c671fd1b11e627714a5ef9e36df5
Transactions (1)
Coinbase18ecdd6794b235…714a5ef9e36df5
1 in β†’ 1 out7.9500 XPM110 B
AUMQRepm…tAfKmdW1
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.

4.227 Γ— 10⁹⁷(98-digit number)
42277227443753734851…31996198198410752000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.227 Γ— 10⁹⁷(98-digit number)
42277227443753734851…31996198198410752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.455 Γ— 10⁹⁷(98-digit number)
84554454887507469702…63992396396821504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.691 Γ— 10⁹⁸(99-digit number)
16910890977501493940…27984792793643008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.382 Γ— 10⁹⁸(99-digit number)
33821781955002987881…55969585587286016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.764 Γ— 10⁹⁸(99-digit number)
67643563910005975762…11939171174572032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.352 Γ— 10⁹⁹(100-digit number)
13528712782001195152…23878342349144064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.705 Γ— 10⁹⁹(100-digit number)
27057425564002390304…47756684698288128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.411 Γ— 10⁹⁹(100-digit number)
54114851128004780609…95513369396576256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.082 Γ— 10¹⁰⁰(101-digit number)
10822970225600956121…91026738793152512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.164 Γ— 10¹⁰⁰(101-digit number)
21645940451201912243…82053477586305024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.329 Γ— 10¹⁰⁰(101-digit number)
43291880902403824487…64106955172610048001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3008055

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 e9289c2d9d75de83560acfefaa33da21d2bb8939e51a5665b98ff20b8b3a9bd5

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 #3,008,055 on Chainz β†—
Circulating Supply:57,993,407 XPMΒ·at block #6,843,629 Β· updates every 60s
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