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Home/Chain Registry/Block #2,238,133

Block #2,238,133

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 2:05:33 PM Β· Difficulty 10.9461 Β· 4,598,408 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bdb8591036c681edde42084df66ff1f2845a64034e2b7f51eb3f8d5ee55a4988
View on Chainz β†—

Difficulty

10.946107

Transactions

1

Size

199 B

Version

2

Bits

0af23412

Nonce

1,403,707,085

Timestamp

8/5/2017, 2:05:33 PM

Confirmations

4,598,408

Merkle Root

0bdcc6d39aea0bfd2018fd2706feb4ba9edad41e60748d121d2a6250a446089e
Transactions (1)
Coinbase0bdcc6d39aea0b…2a6250a446089e
1 in β†’ 1 out8.3300 XPM109 B
AT6ZEfYS…gmZuHiSf
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.

9.397 Γ— 10⁹³(94-digit number)
93972562942460060209…27043576121000864990
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
9.397 Γ— 10⁹³(94-digit number)
93972562942460060209…27043576121000864991
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.879 Γ— 10⁹⁴(95-digit number)
18794512588492012041…54087152242001729981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.758 Γ— 10⁹⁴(95-digit number)
37589025176984024083…08174304484003459961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.517 Γ— 10⁹⁴(95-digit number)
75178050353968048167…16348608968006919921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.503 Γ— 10⁹⁡(96-digit number)
15035610070793609633…32697217936013839841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.007 Γ— 10⁹⁡(96-digit number)
30071220141587219267…65394435872027679681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.014 Γ— 10⁹⁡(96-digit number)
60142440283174438534…30788871744055359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.202 Γ— 10⁹⁢(97-digit number)
12028488056634887706…61577743488110718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.405 Γ— 10⁹⁢(97-digit number)
24056976113269775413…23155486976221437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.811 Γ— 10⁹⁢(97-digit number)
48113952226539550827…46310973952442874881
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 2238133

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 bdb8591036c681edde42084df66ff1f2845a64034e2b7f51eb3f8d5ee55a4988

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 #2,238,133 on Chainz β†—
Circulating Supply:57,936,592 XPMΒ·at block #6,836,540 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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