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Home/Chain Registry/Block #2,177,872

Block #2,177,872

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/25/2017, 7:23:56 PM Β· Difficulty 10.9243 Β· 4,667,784 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d9396a77a44120449edd58518adb117401b7f235faace4c3a8b8c9e3e80ef141
View on Chainz β†—

Difficulty

10.924307

Transactions

1

Size

198 B

Version

2

Bits

0aec9f5a

Nonce

29,979,463

Timestamp

6/25/2017, 7:23:56 PM

Confirmations

4,667,784

Merkle Root

adedf272d613defcd43900d72232fa04c639ea57a302685a32b7615241e0d290
Transactions (1)
Coinbaseadedf272d613de…b7615241e0d290
1 in β†’ 1 out8.3700 XPM109 B
AQXvTc7A…t5kzpXdY
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.

2.195 Γ— 10⁹²(93-digit number)
21959132684172423108…15818333123910314900
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
2.195 Γ— 10⁹²(93-digit number)
21959132684172423108…15818333123910314901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.391 Γ— 10⁹²(93-digit number)
43918265368344846216…31636666247820629801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.783 Γ— 10⁹²(93-digit number)
87836530736689692432…63273332495641259601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.756 Γ— 10⁹³(94-digit number)
17567306147337938486…26546664991282519201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.513 Γ— 10⁹³(94-digit number)
35134612294675876972…53093329982565038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.026 Γ— 10⁹³(94-digit number)
70269224589351753945…06186659965130076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.405 Γ— 10⁹⁴(95-digit number)
14053844917870350789…12373319930260153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.810 Γ— 10⁹⁴(95-digit number)
28107689835740701578…24746639860520307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.621 Γ— 10⁹⁴(95-digit number)
56215379671481403156…49493279721040614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.124 Γ— 10⁹⁡(96-digit number)
11243075934296280631…98986559442081228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.248 Γ— 10⁹⁡(96-digit number)
22486151868592561262…97973118884162457601
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 2177872

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 d9396a77a44120449edd58518adb117401b7f235faace4c3a8b8c9e3e80ef141

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 #2,177,872 on Chainz β†—
Circulating Supply:58,009,697 XPMΒ·at block #6,845,655 Β· updates every 60s
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