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Home/Chain Registry/Block #1,246,315

Block #1,246,315

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2015, 11:42:13 AM Β· Difficulty 10.7504 Β· 5,598,694 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cf02fd8d3aca87c5b2bbe73cbbdf9320e26104e5c5ee0a7dd607d23e9bb8f74f
View on Chainz β†—

Difficulty

10.750449

Transactions

1

Size

199 B

Version

2

Bits

0ac01d67

Nonce

822,784,713

Timestamp

9/21/2015, 11:42:13 AM

Confirmations

5,598,694

Merkle Root

3a2b789f30f8685c528bfec7c394b3014e3703ee0c59290985d6b69717b14881
Transactions (1)
Coinbase3a2b789f30f868…d6b69717b14881
1 in β†’ 1 out8.6400 XPM109 B
ANJ9Qsqw…Bhuu86SL
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.

3.325 Γ— 10⁹⁡(96-digit number)
33252763344948594939…24561149804269084160
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
3.325 Γ— 10⁹⁡(96-digit number)
33252763344948594939…24561149804269084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.650 Γ— 10⁹⁡(96-digit number)
66505526689897189879…49122299608538168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.330 Γ— 10⁹⁢(97-digit number)
13301105337979437975…98244599217076336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.660 Γ— 10⁹⁢(97-digit number)
26602210675958875951…96489198434152673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.320 Γ— 10⁹⁢(97-digit number)
53204421351917751903…92978396868305346561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.064 Γ— 10⁹⁷(98-digit number)
10640884270383550380…85956793736610693121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.128 Γ— 10⁹⁷(98-digit number)
21281768540767100761…71913587473221386241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.256 Γ— 10⁹⁷(98-digit number)
42563537081534201522…43827174946442772481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.512 Γ— 10⁹⁷(98-digit number)
85127074163068403045…87654349892885544961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.702 Γ— 10⁹⁸(99-digit number)
17025414832613680609…75308699785771089921
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 1246315

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 cf02fd8d3aca87c5b2bbe73cbbdf9320e26104e5c5ee0a7dd607d23e9bb8f74f

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 #1,246,315 on Chainz β†—
Circulating Supply:58,004,494 XPMΒ·at block #6,845,008 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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