XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #233,407

Block #233,407

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2013, 5:08:35 PM Β· Difficulty 9.9425 Β· 6,591,523 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1e9b5ae4b3dcc3f10783d49410663abf1340bbb5cee93d0d33cf1e68caab82e
View on Chainz β†—

Height

#233,407

Difficulty

9.942464

Transactions

1

Size

199 B

Version

2

Bits

09f14559

Nonce

58,301

Timestamp

10/29/2013, 5:08:35 PM

Confirmations

6,591,523

Merkle Root

d686de1e6f3dd92f01656337892655dcd9f1b8690bdcb60f6259500f1a11e071
Transactions (1)
Coinbased686de1e6f3dd9…59500f1a11e071
1 in β†’ 1 out10.1000 XPM109 B
AYkJwj7K…a96vudhF
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.

3.466 Γ— 10⁹³(94-digit number)
34665423106355124983…87465933981145295140
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
3.466 Γ— 10⁹³(94-digit number)
34665423106355124983…87465933981145295141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.933 Γ— 10⁹³(94-digit number)
69330846212710249967…74931867962290590281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.386 Γ— 10⁹⁴(95-digit number)
13866169242542049993…49863735924581180561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.773 Γ— 10⁹⁴(95-digit number)
27732338485084099986…99727471849162361121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.546 Γ— 10⁹⁴(95-digit number)
55464676970168199973…99454943698324722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.109 Γ— 10⁹⁡(96-digit number)
11092935394033639994…98909887396649444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.218 Γ— 10⁹⁡(96-digit number)
22185870788067279989…97819774793298888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.437 Γ— 10⁹⁡(96-digit number)
44371741576134559978…95639549586597777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.874 Γ— 10⁹⁡(96-digit number)
88743483152269119957…91279099173195555841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.774 Γ— 10⁹⁢(97-digit number)
17748696630453823991…82558198346391111681
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 233407

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 c1e9b5ae4b3dcc3f10783d49410663abf1340bbb5cee93d0d33cf1e68caab82e

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 #233,407 on Chainz β†—
Circulating Supply:57,843,516 XPMΒ·at block #6,824,929 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy