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Home/Chain Registry/Block #2,877,972

Block #2,877,972

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2018, 11:08:06 AM Β· Difficulty 11.6459 Β· 3,962,068 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9175f5fb779219758a107ba3596fd99bf94ff9548af0cc943f0ba9db5f9ababf
View on Chainz β†—

Difficulty

11.645930

Transactions

1

Size

200 B

Version

2

Bits

0ba55bb0

Nonce

794,125,325

Timestamp

10/12/2018, 11:08:06 AM

Confirmations

3,962,068

Merkle Root

0cf153b0585972634c60d016710cfce3978278438db0851bb26e8aa5a030a21c
Transactions (1)
Coinbase0cf153b0585972…6e8aa5a030a21c
1 in β†’ 1 out7.3600 XPM110 B
ARq8GsEN…J21piGMB
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.

1.110 Γ— 10⁹⁡(96-digit number)
11108470968190175297…97974665193985779200
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
1.110 Γ— 10⁹⁡(96-digit number)
11108470968190175297…97974665193985779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.221 Γ— 10⁹⁡(96-digit number)
22216941936380350594…95949330387971558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.443 Γ— 10⁹⁡(96-digit number)
44433883872760701188…91898660775943116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.886 Γ— 10⁹⁡(96-digit number)
88867767745521402376…83797321551886233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.777 Γ— 10⁹⁢(97-digit number)
17773553549104280475…67594643103772467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.554 Γ— 10⁹⁢(97-digit number)
35547107098208560950…35189286207544934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.109 Γ— 10⁹⁢(97-digit number)
71094214196417121901…70378572415089868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.421 Γ— 10⁹⁷(98-digit number)
14218842839283424380…40757144830179737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.843 Γ— 10⁹⁷(98-digit number)
28437685678566848760…81514289660359475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.687 Γ— 10⁹⁷(98-digit number)
56875371357133697521…63028579320718950401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.137 Γ— 10⁹⁸(99-digit number)
11375074271426739504…26057158641437900801
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 2877972

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 9175f5fb779219758a107ba3596fd99bf94ff9548af0cc943f0ba9db5f9ababf

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 #2,877,972 on Chainz β†—
Circulating Supply:57,964,634 XPMΒ·at block #6,840,039 Β· updates every 60s
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