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Home/Chain Registry/Block #1,515,911

Block #1,515,911

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/28/2016, 12:37:59 PM Β· Difficulty 10.5999 Β· 5,327,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81a86b910a39bf8c4d6cf7f0eb7c882bdfaf397a80e98482bfbc0cf0885526b3
View on Chainz β†—

Difficulty

10.599870

Transactions

1

Size

201 B

Version

2

Bits

0a99910e

Nonce

132,442,054

Timestamp

3/28/2016, 12:37:59 PM

Confirmations

5,327,087

Merkle Root

7a87b73af3b6276c598599a923ba978de2a5586de4958f4ef32385d1c3a2dd4f
Transactions (1)
Coinbase7a87b73af3b627…2385d1c3a2dd4f
1 in β†’ 1 out8.8900 XPM110 B
ARHsxCb4…D4Et7Czf
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.

1.147 Γ— 10⁹⁷(98-digit number)
11471596435183436501…89492781487756083200
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.147 Γ— 10⁹⁷(98-digit number)
11471596435183436501…89492781487756083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.294 Γ— 10⁹⁷(98-digit number)
22943192870366873002…78985562975512166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.588 Γ— 10⁹⁷(98-digit number)
45886385740733746005…57971125951024332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.177 Γ— 10⁹⁷(98-digit number)
91772771481467492010…15942251902048665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.835 Γ— 10⁹⁸(99-digit number)
18354554296293498402…31884503804097331199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.670 Γ— 10⁹⁸(99-digit number)
36709108592586996804…63769007608194662399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.341 Γ— 10⁹⁸(99-digit number)
73418217185173993608…27538015216389324799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁹(100-digit number)
14683643437034798721…55076030432778649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.936 Γ— 10⁹⁹(100-digit number)
29367286874069597443…10152060865557299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.873 Γ— 10⁹⁹(100-digit number)
58734573748139194886…20304121731114598399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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
UncommonChain length 10
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1515911

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 81a86b910a39bf8c4d6cf7f0eb7c882bdfaf397a80e98482bfbc0cf0885526b3

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 #1,515,911 on Chainz β†—
Circulating Supply:57,988,339 XPMΒ·at block #6,842,997 Β· updates every 60s
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