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Home/Chain Registry/Block #2,988,600

Block #2,988,600

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/30/2018, 8:30:17 PM Β· Difficulty 11.2692 Β· 3,845,155 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2ef579833b7863a5c7fddaca0cb0ce6dadae2b030f1bba15137776cb5a2e5db
View on Chainz β†—

Difficulty

11.269205

Transactions

1

Size

200 B

Version

2

Bits

0b44ea9d

Nonce

1,555,762,826

Timestamp

12/30/2018, 8:30:17 PM

Confirmations

3,845,155

Merkle Root

4b0571e2a39a9be5421b0ebb05f66bbc5c15d87cc42d6d841a5c18681c319007
Transactions (1)
Coinbase4b0571e2a39a9b…5c18681c319007
1 in β†’ 1 out7.8600 XPM110 B
AUhjokok…k5m93PZR
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.

2.225 Γ— 10⁹⁴(95-digit number)
22257492482590451331…33642318832917504000
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
2.225 Γ— 10⁹⁴(95-digit number)
22257492482590451331…33642318832917504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.451 Γ— 10⁹⁴(95-digit number)
44514984965180902663…67284637665835008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.902 Γ— 10⁹⁴(95-digit number)
89029969930361805327…34569275331670016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.780 Γ— 10⁹⁡(96-digit number)
17805993986072361065…69138550663340032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.561 Γ— 10⁹⁡(96-digit number)
35611987972144722131…38277101326680064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.122 Γ— 10⁹⁡(96-digit number)
71223975944289444262…76554202653360128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.424 Γ— 10⁹⁢(97-digit number)
14244795188857888852…53108405306720256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.848 Γ— 10⁹⁢(97-digit number)
28489590377715777704…06216810613440512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.697 Γ— 10⁹⁢(97-digit number)
56979180755431555409…12433621226881024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.139 Γ— 10⁹⁷(98-digit number)
11395836151086311081…24867242453762048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.279 Γ— 10⁹⁷(98-digit number)
22791672302172622163…49734484907524096001
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 2988600

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 a2ef579833b7863a5c7fddaca0cb0ce6dadae2b030f1bba15137776cb5a2e5db

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 #2,988,600 on Chainz β†—
Circulating Supply:57,914,257 XPMΒ·at block #6,833,754 Β· updates every 60s
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