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Home/Chain Registry/Block #1,145,561

Block #1,145,561

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/8/2015, 10:04:18 PM Β· Difficulty 10.9309 Β· 5,696,922 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5dbdec7a4f779affbbd9a103e39f3542dbc04bf5ff961d7fe1993bb89b8e4617
View on Chainz β†—

Difficulty

10.930936

Transactions

1

Size

201 B

Version

2

Bits

0aee51d1

Nonce

1,141,120,205

Timestamp

7/8/2015, 10:04:18 PM

Confirmations

5,696,922

Merkle Root

8eaba519f6a60c975542a5b76d701ccef10fdf1915e0be89e9d4869c5769045d
Transactions (1)
Coinbase8eaba519f6a60c…d4869c5769045d
1 in β†’ 1 out8.3600 XPM110 B
ARa5CnZJ…LiqJCRmo
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.

3.129 Γ— 10⁹⁢(97-digit number)
31293434494656550216…90875588945179576320
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
3.129 Γ— 10⁹⁢(97-digit number)
31293434494656550216…90875588945179576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.258 Γ— 10⁹⁢(97-digit number)
62586868989313100433…81751177890359152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12517373797862620086…63502355780718305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.503 Γ— 10⁹⁷(98-digit number)
25034747595725240173…27004711561436610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.006 Γ— 10⁹⁷(98-digit number)
50069495191450480346…54009423122873221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.001 Γ— 10⁹⁸(99-digit number)
10013899038290096069…08018846245746442241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.002 Γ— 10⁹⁸(99-digit number)
20027798076580192138…16037692491492884481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.005 Γ— 10⁹⁸(99-digit number)
40055596153160384277…32075384982985768961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.011 Γ— 10⁹⁸(99-digit number)
80111192306320768554…64150769965971537921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.602 Γ— 10⁹⁹(100-digit number)
16022238461264153710…28301539931943075841
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 1145561

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 5dbdec7a4f779affbbd9a103e39f3542dbc04bf5ff961d7fe1993bb89b8e4617

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 #1,145,561 on Chainz β†—
Circulating Supply:57,984,282 XPMΒ·at block #6,842,482 Β· updates every 60s
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