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Block #2,259,612

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2017, 3:23:28 AM Β· Difficulty 10.9520 Β· 4,581,178 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77221b69bfefdeeabf6fed17dc571e22c7da38a8ca974e2cefbcb72bafa7fd75
View on Chainz β†—

Difficulty

10.952015

Transactions

1

Size

200 B

Version

2

Bits

0af3b747

Nonce

646,423,483

Timestamp

8/20/2017, 3:23:28 AM

Confirmations

4,581,178

Merkle Root

5c2009c74c3d8c0170a8b6c67ece84e3b82bb8a2d8f5360240d66838555d0274
Transactions (1)
Coinbase5c2009c74c3d8c…d66838555d0274
1 in β†’ 1 out8.3200 XPM110 B
AXLzGzQV…T5xMfTo5
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.

3.168 Γ— 10⁹⁴(95-digit number)
31686786522520596725…79563981333286832080
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
3.168 Γ— 10⁹⁴(95-digit number)
31686786522520596725…79563981333286832081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.337 Γ— 10⁹⁴(95-digit number)
63373573045041193451…59127962666573664161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.267 Γ— 10⁹⁡(96-digit number)
12674714609008238690…18255925333147328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.534 Γ— 10⁹⁡(96-digit number)
25349429218016477380…36511850666294656641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.069 Γ— 10⁹⁡(96-digit number)
50698858436032954760…73023701332589313281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10139771687206590952…46047402665178626561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20279543374413181904…92094805330357253121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.055 Γ— 10⁹⁢(97-digit number)
40559086748826363808…84189610660714506241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.111 Γ— 10⁹⁢(97-digit number)
81118173497652727617…68379221321429012481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.622 Γ— 10⁹⁷(98-digit number)
16223634699530545523…36758442642858024961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.244 Γ— 10⁹⁷(98-digit number)
32447269399061091047…73516885285716049921
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 2259612

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 77221b69bfefdeeabf6fed17dc571e22c7da38a8ca974e2cefbcb72bafa7fd75

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 #2,259,612 on Chainz β†—
Circulating Supply:57,970,667 XPMΒ·at block #6,840,789 Β· updates every 60s
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