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Home/Chain Registry/Block #3,008,427

Block #3,008,427

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2019, 10:23:28 PM Β· Difficulty 11.2021 Β· 3,834,648 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e3e2d6396e2cd7ca6138d4108c8253e528b30702c3ae10ef154affa58b4dc46
View on Chainz β†—

Difficulty

11.202105

Transactions

1

Size

200 B

Version

2

Bits

0b33bd2f

Nonce

553,301,295

Timestamp

1/13/2019, 10:23:28 PM

Confirmations

3,834,648

Merkle Root

65fa31bc593150fe4a57531b5c824a0dd67cedd028dcb142d37e94a17eab7cc7
Transactions (1)
Coinbase65fa31bc593150…7e94a17eab7cc7
1 in β†’ 1 out7.9600 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.

4.230 Γ— 10⁹⁴(95-digit number)
42308444315646527680…81859520704063174160
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
4.230 Γ— 10⁹⁴(95-digit number)
42308444315646527680…81859520704063174161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.461 Γ— 10⁹⁴(95-digit number)
84616888631293055361…63719041408126348321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.692 Γ— 10⁹⁡(96-digit number)
16923377726258611072…27438082816252696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.384 Γ— 10⁹⁡(96-digit number)
33846755452517222144…54876165632505393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.769 Γ— 10⁹⁡(96-digit number)
67693510905034444289…09752331265010786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.353 Γ— 10⁹⁢(97-digit number)
13538702181006888857…19504662530021573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.707 Γ— 10⁹⁢(97-digit number)
27077404362013777715…39009325060043146241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.415 Γ— 10⁹⁢(97-digit number)
54154808724027555431…78018650120086292481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.083 Γ— 10⁹⁷(98-digit number)
10830961744805511086…56037300240172584961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.166 Γ— 10⁹⁷(98-digit number)
21661923489611022172…12074600480345169921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.332 Γ— 10⁹⁷(98-digit number)
43323846979222044345…24149200960690339841
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 3008427

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 5e3e2d6396e2cd7ca6138d4108c8253e528b30702c3ae10ef154affa58b4dc46

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 #3,008,427 on Chainz β†—
Circulating Supply:57,988,960 XPMΒ·at block #6,843,074 Β· updates every 60s
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