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Home/Chain Registry/Block #2,130,013

Block #2,130,013

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/24/2017, 3:34:44 AM Β· Difficulty 10.9094 Β· 4,708,306 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6abe5bb9e65f89452ca661baace44f3c63b102effb0b49008ee80f6778369c1
View on Chainz β†—

Difficulty

10.909432

Transactions

2

Size

425 B

Version

2

Bits

0ae8d088

Nonce

1,309,244,215

Timestamp

5/24/2017, 3:34:44 AM

Confirmations

4,708,306

Merkle Root

a9720c8453a6e2cbaad81b477927fcd0c01cb8d5ef8f7d4c9b03f285a3dfff8d
Transactions (2)
Coinbase1b163299ad4f46…37a5ccf1b541b8
1 in β†’ 1 out8.4000 XPM110 B
Acr4nBhH…1WVxBk1z
056d14d1357fb4…3328e117cfb01f
1 in β†’ 2 out203320.7381 XPM225 B
AL4g3QwY…mpj35dTUAdGyyHnu…2SXXwRyk
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.

1.431 Γ— 10⁹⁴(95-digit number)
14311439100294818115…50782747438531338460
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
1.431 Γ— 10⁹⁴(95-digit number)
14311439100294818115…50782747438531338459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.862 Γ— 10⁹⁴(95-digit number)
28622878200589636231…01565494877062676919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.724 Γ— 10⁹⁴(95-digit number)
57245756401179272463…03130989754125353839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.144 Γ— 10⁹⁡(96-digit number)
11449151280235854492…06261979508250707679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.289 Γ— 10⁹⁡(96-digit number)
22898302560471708985…12523959016501415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.579 Γ— 10⁹⁡(96-digit number)
45796605120943417970…25047918033002830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.159 Γ— 10⁹⁡(96-digit number)
91593210241886835941…50095836066005661439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.831 Γ— 10⁹⁢(97-digit number)
18318642048377367188…00191672132011322879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.663 Γ— 10⁹⁢(97-digit number)
36637284096754734376…00383344264022645759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.327 Γ— 10⁹⁢(97-digit number)
73274568193509468752…00766688528045291519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.465 Γ— 10⁹⁷(98-digit number)
14654913638701893750…01533377056090583039
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 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
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 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 2130013

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 e6abe5bb9e65f89452ca661baace44f3c63b102effb0b49008ee80f6778369c1

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 #2,130,013 on Chainz β†—
Circulating Supply:57,950,827 XPMΒ·at block #6,838,318 Β· updates every 60s
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