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Home/Chain Registry/Block #2,135,864

Block #2,135,864

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2017, 3:04:56 PM Β· Difficulty 10.8982 Β· 4,706,770 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
841566ff01d25eca3a044eee5cf2f9e4952b165f158fa777bb2a87fafbd319ee
View on Chainz β†—

Difficulty

10.898180

Transactions

1

Size

200 B

Version

2

Bits

0ae5ef26

Nonce

964,098,480

Timestamp

5/28/2017, 3:04:56 PM

Confirmations

4,706,770

Merkle Root

45d24c10fe16d84ca181f7aa856ae86b4357131657109d7bb75476861b61e213
Transactions (1)
Coinbase45d24c10fe16d8…5476861b61e213
1 in β†’ 1 out8.4100 XPM109 B
AXmJzGdZ…ePNgLY88
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.

3.789 Γ— 10⁹⁢(97-digit number)
37893654037979328413…98162514894728104960
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.789 Γ— 10⁹⁢(97-digit number)
37893654037979328413…98162514894728104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.578 Γ— 10⁹⁢(97-digit number)
75787308075958656826…96325029789456209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁷(98-digit number)
15157461615191731365…92650059578912419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.031 Γ— 10⁹⁷(98-digit number)
30314923230383462730…85300119157824839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.062 Γ— 10⁹⁷(98-digit number)
60629846460766925461…70600238315649679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁸(99-digit number)
12125969292153385092…41200476631299358719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁸(99-digit number)
24251938584306770184…82400953262598717439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.850 Γ— 10⁹⁸(99-digit number)
48503877168613540368…64801906525197434879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.700 Γ— 10⁹⁸(99-digit number)
97007754337227080737…29603813050394869759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.940 Γ— 10⁹⁹(100-digit number)
19401550867445416147…59207626100789739519
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2135864

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 841566ff01d25eca3a044eee5cf2f9e4952b165f158fa777bb2a87fafbd319ee

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 #2,135,864 on Chainz β†—
Circulating Supply:57,985,505 XPMΒ·at block #6,842,633 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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