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Home/Chain Registry/Block #2,772,564

Block #2,772,564

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/31/2018, 1:22:36 AM Β· Difficulty 11.6624 Β· 4,071,239 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c80e4ea9b7939182282c729e0afb054aaffe44e44ad87ababc8f239ea8078951
View on Chainz β†—

Difficulty

11.662381

Transactions

1

Size

200 B

Version

2

Bits

0ba991ce

Nonce

755,786,655

Timestamp

7/31/2018, 1:22:36 AM

Confirmations

4,071,239

Merkle Root

960e6b2d9b67554c10288929f239dc9e2751810982aef15b4a5df91e1ad7baf0
Transactions (1)
Coinbase960e6b2d9b6755…5df91e1ad7baf0
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.886 Γ— 10⁹⁴(95-digit number)
58861162761336398388…86484773706651250720
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
5.886 Γ— 10⁹⁴(95-digit number)
58861162761336398388…86484773706651250721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.177 Γ— 10⁹⁡(96-digit number)
11772232552267279677…72969547413302501441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.354 Γ— 10⁹⁡(96-digit number)
23544465104534559355…45939094826605002881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.708 Γ— 10⁹⁡(96-digit number)
47088930209069118710…91878189653210005761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.417 Γ— 10⁹⁡(96-digit number)
94177860418138237421…83756379306420011521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.883 Γ— 10⁹⁢(97-digit number)
18835572083627647484…67512758612840023041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.767 Γ— 10⁹⁢(97-digit number)
37671144167255294968…35025517225680046081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.534 Γ— 10⁹⁢(97-digit number)
75342288334510589937…70051034451360092161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.506 Γ— 10⁹⁷(98-digit number)
15068457666902117987…40102068902720184321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.013 Γ— 10⁹⁷(98-digit number)
30136915333804235974…80204137805440368641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.027 Γ— 10⁹⁷(98-digit number)
60273830667608471949…60408275610880737281
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 2772564

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 c80e4ea9b7939182282c729e0afb054aaffe44e44ad87ababc8f239ea8078951

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 #2,772,564 on Chainz β†—
Circulating Supply:57,994,801 XPMΒ·at block #6,843,802 Β· updates every 60s
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