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Home/Chain Registry/Block #1,412,211

Block #1,412,211

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2016, 11:03:06 PM Β· Difficulty 10.8042 Β· 5,415,046 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
027b97ad6cd0b1698ef4ec43d8e8fd6cbed41c9ef636ed42d5f350fbd841037f
View on Chainz β†—

Difficulty

10.804219

Transactions

1

Size

198 B

Version

2

Bits

0acde152

Nonce

902,443,692

Timestamp

1/13/2016, 11:03:06 PM

Confirmations

5,415,046

Merkle Root

7d09b5320951a3cc30185a01acef30c8bea84017a27b82b590383218aeaf00dc
Transactions (1)
Coinbase7d09b5320951a3…383218aeaf00dc
1 in β†’ 1 out8.5500 XPM109 B
AaXjVzia…3Tbzhk3o
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.

1.212 Γ— 10⁹²(93-digit number)
12124922047858012233…64112129066103331840
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
1.212 Γ— 10⁹²(93-digit number)
12124922047858012233…64112129066103331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.424 Γ— 10⁹²(93-digit number)
24249844095716024467…28224258132206663681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.849 Γ— 10⁹²(93-digit number)
48499688191432048935…56448516264413327361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.699 Γ— 10⁹²(93-digit number)
96999376382864097870…12897032528826654721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.939 Γ— 10⁹³(94-digit number)
19399875276572819574…25794065057653309441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.879 Γ— 10⁹³(94-digit number)
38799750553145639148…51588130115306618881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.759 Γ— 10⁹³(94-digit number)
77599501106291278296…03176260230613237761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.551 Γ— 10⁹⁴(95-digit number)
15519900221258255659…06352520461226475521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.103 Γ— 10⁹⁴(95-digit number)
31039800442516511318…12705040922452951041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.207 Γ— 10⁹⁴(95-digit number)
62079600885033022637…25410081844905902081
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 1412211

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 027b97ad6cd0b1698ef4ec43d8e8fd6cbed41c9ef636ed42d5f350fbd841037f

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 #1,412,211 on Chainz β†—
Circulating Supply:57,862,159 XPMΒ·at block #6,827,256 Β· updates every 60s
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