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Home/Chain Registry/Block #2,238,156

Block #2,238,156

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 2:26:14 PM Β· Difficulty 10.9461 Β· 4,601,043 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
63b3a860c8ca3e768abd935e4237ed91a720e33c33630f3809173ce0ffa76c8e
View on Chainz β†—

Difficulty

10.946132

Transactions

1

Size

199 B

Version

2

Bits

0af235b0

Nonce

1,393,369,579

Timestamp

8/5/2017, 2:26:14 PM

Confirmations

4,601,043

Merkle Root

5a3cc70b3d3c3203b1cf2d64c5e5060dcf664cec1944a3f8f358be4df586c9e5
Transactions (1)
Coinbase5a3cc70b3d3c32…58be4df586c9e5
1 in β†’ 1 out8.3300 XPM110 B
APV3AAxh…mdgwGmGc
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.

6.799 Γ— 10⁹¹(92-digit number)
67998015571260163956…05162884080712538360
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
6.799 Γ— 10⁹¹(92-digit number)
67998015571260163956…05162884080712538361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.359 Γ— 10⁹²(93-digit number)
13599603114252032791…10325768161425076721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.719 Γ— 10⁹²(93-digit number)
27199206228504065582…20651536322850153441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.439 Γ— 10⁹²(93-digit number)
54398412457008131164…41303072645700306881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.087 Γ— 10⁹³(94-digit number)
10879682491401626232…82606145291400613761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.175 Γ— 10⁹³(94-digit number)
21759364982803252465…65212290582801227521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.351 Γ— 10⁹³(94-digit number)
43518729965606504931…30424581165602455041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.703 Γ— 10⁹³(94-digit number)
87037459931213009863…60849162331204910081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.740 Γ— 10⁹⁴(95-digit number)
17407491986242601972…21698324662409820161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.481 Γ— 10⁹⁴(95-digit number)
34814983972485203945…43396649324819640321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.962 Γ— 10⁹⁴(95-digit number)
69629967944970407890…86793298649639280641
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 2238156

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 63b3a860c8ca3e768abd935e4237ed91a720e33c33630f3809173ce0ffa76c8e

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 #2,238,156 on Chainz β†—
Circulating Supply:57,957,871 XPMΒ·at block #6,839,198 Β· updates every 60s
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