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Home/Chain Registry/Block #2,770,685

Block #2,770,685

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2018, 6:40:55 PM Β· Difficulty 11.6597 Β· 4,068,672 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7ce12a94cb7e9fb017614f6de0fbae5ca0f984199b489746f02078231de4a25
View on Chainz β†—

Difficulty

11.659666

Transactions

1

Size

200 B

Version

2

Bits

0ba8dfe7

Nonce

737,586,767

Timestamp

7/29/2018, 6:40:55 PM

Confirmations

4,068,672

Merkle Root

f19993af8ae5bce551ae5612fc0ccf606c9b63e99c73d6399bdd1ae6ec07d29b
Transactions (1)
Coinbasef19993af8ae5bc…dd1ae6ec07d29b
1 in β†’ 1 out7.3400 XPM109 B
AHevwhJL…ryeXXZyN
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.

1.101 Γ— 10⁹⁢(97-digit number)
11011703278154171042…73301632512180203520
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
1.101 Γ— 10⁹⁢(97-digit number)
11011703278154171042…73301632512180203521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.202 Γ— 10⁹⁢(97-digit number)
22023406556308342085…46603265024360407041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.404 Γ— 10⁹⁢(97-digit number)
44046813112616684170…93206530048720814081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.809 Γ— 10⁹⁢(97-digit number)
88093626225233368340…86413060097441628161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.761 Γ— 10⁹⁷(98-digit number)
17618725245046673668…72826120194883256321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.523 Γ— 10⁹⁷(98-digit number)
35237450490093347336…45652240389766512641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.047 Γ— 10⁹⁷(98-digit number)
70474900980186694672…91304480779533025281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.409 Γ— 10⁹⁸(99-digit number)
14094980196037338934…82608961559066050561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.818 Γ— 10⁹⁸(99-digit number)
28189960392074677869…65217923118132101121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.637 Γ— 10⁹⁸(99-digit number)
56379920784149355738…30435846236264202241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.127 Γ— 10⁹⁹(100-digit number)
11275984156829871147…60871692472528404481
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 2770685

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 a7ce12a94cb7e9fb017614f6de0fbae5ca0f984199b489746f02078231de4a25

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 #2,770,685 on Chainz β†—
Circulating Supply:57,959,135 XPMΒ·at block #6,839,356 Β· updates every 60s
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