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Home/Chain Registry/Block #1,411,918

Block #1,411,918

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2016, 6:01:26 PM Β· Difficulty 10.8047 Β· 5,433,732 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2682f0445d653dad38ef47d21f927315b1f4c1e15ee0db1742158fd8b6300734
View on Chainz β†—

Difficulty

10.804665

Transactions

2

Size

1.28 KB

Version

2

Bits

0acdfe82

Nonce

298,230,340

Timestamp

1/13/2016, 6:01:26 PM

Confirmations

5,433,732

Merkle Root

6cde93127c60535d5558fd1e15e76caa47eb92136fa9b67d61e0cac00f37ab9b
Transactions (2)
Coinbasee4f3400e4eed5e…16d2d92d9c567e
1 in β†’ 1 out8.5700 XPM109 B
ANd6Zc6h…i3pBrHAS
4dc7a5e193d1b1…1d042f34f4a028
7 in β†’ 2 out1339.7291 XPM1.09 KB
AVaB5s3y…P2pW1DebAR1ovHYW…i5qGA1Dm
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.

6.154 Γ— 10⁹⁡(96-digit number)
61544414462533488057…42077856156584809600
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
6.154 Γ— 10⁹⁡(96-digit number)
61544414462533488057…42077856156584809601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.230 Γ— 10⁹⁢(97-digit number)
12308882892506697611…84155712313169619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.461 Γ— 10⁹⁢(97-digit number)
24617765785013395222…68311424626339238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.923 Γ— 10⁹⁢(97-digit number)
49235531570026790445…36622849252678476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.847 Γ— 10⁹⁢(97-digit number)
98471063140053580891…73245698505356953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.969 Γ— 10⁹⁷(98-digit number)
19694212628010716178…46491397010713907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.938 Γ— 10⁹⁷(98-digit number)
39388425256021432356…92982794021427814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.877 Γ— 10⁹⁷(98-digit number)
78776850512042864713…85965588042855628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.575 Γ— 10⁹⁸(99-digit number)
15755370102408572942…71931176085711257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.151 Γ— 10⁹⁸(99-digit number)
31510740204817145885…43862352171422515201
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 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
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 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 1411918

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 2682f0445d653dad38ef47d21f927315b1f4c1e15ee0db1742158fd8b6300734

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 #1,411,918 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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