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Home/Chain Registry/Block #2,961,033

Block #2,961,033

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/11/2018, 7:28:10 AM Β· Difficulty 11.3467 Β· 3,880,096 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22273e59a1b4991d91fd50f3e98663ce901aee3659fc465cefe12b762371c99a
View on Chainz β†—

Difficulty

11.346743

Transactions

1

Size

199 B

Version

2

Bits

0b58c42d

Nonce

1,349,053,071

Timestamp

12/11/2018, 7:28:10 AM

Confirmations

3,880,096

Merkle Root

6b442e9ab53054dbd277de7f267426533a3588d9d5e4709400a80f9ee8af27d0
Transactions (1)
Coinbase6b442e9ab53054…a80f9ee8af27d0
1 in β†’ 1 out7.7500 XPM109 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.

2.288 Γ— 10⁹⁡(96-digit number)
22883156902405338743…12285387816627251200
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
2.288 Γ— 10⁹⁡(96-digit number)
22883156902405338743…12285387816627251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.576 Γ— 10⁹⁡(96-digit number)
45766313804810677486…24570775633254502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.153 Γ— 10⁹⁡(96-digit number)
91532627609621354973…49141551266509004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.830 Γ— 10⁹⁢(97-digit number)
18306525521924270994…98283102533018009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.661 Γ— 10⁹⁢(97-digit number)
36613051043848541989…96566205066036019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.322 Γ— 10⁹⁢(97-digit number)
73226102087697083978…93132410132072038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.464 Γ— 10⁹⁷(98-digit number)
14645220417539416795…86264820264144076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.929 Γ— 10⁹⁷(98-digit number)
29290440835078833591…72529640528288153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.858 Γ— 10⁹⁷(98-digit number)
58580881670157667182…45059281056576307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.171 Γ— 10⁹⁸(99-digit number)
11716176334031533436…90118562113152614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.343 Γ— 10⁹⁸(99-digit number)
23432352668063066873…80237124226305228801
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 2961033

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 22273e59a1b4991d91fd50f3e98663ce901aee3659fc465cefe12b762371c99a

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 #2,961,033 on Chainz β†—
Circulating Supply:57,973,401 XPMΒ·at block #6,841,128 Β· updates every 60s
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