XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #29,680

Block #29,680

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 4:19:44 PM Β· Difficulty 7.9852 Β· 6,781,930 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
92e2963fa591d998a75bf16af84ba70290c3adc9910c00e91022fd3dc7810461
View on Chainz β†—

Height

#29,680

Difficulty

7.985209

Transactions

1

Size

198 B

Version

2

Bits

07fc36b0

Nonce

1,104

Timestamp

7/13/2013, 4:19:44 PM

Confirmations

6,781,930

Merkle Root

622fd8a2e9fc66c4f9a1bb3c015855da1cd2f2593d9b26174867c206e28e158a
Transactions (1)
Coinbase622fd8a2e9fc66…67c206e28e158a
1 in β†’ 1 out15.6600 XPM108 B
APY1J1ZY…FaUv3anE
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.

1.019 Γ— 10⁹⁴(95-digit number)
10193603723845018296…33605631044075596480
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
1.019 Γ— 10⁹⁴(95-digit number)
10193603723845018296…33605631044075596481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.038 Γ— 10⁹⁴(95-digit number)
20387207447690036592…67211262088151192961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.077 Γ— 10⁹⁴(95-digit number)
40774414895380073184…34422524176302385921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.154 Γ— 10⁹⁴(95-digit number)
81548829790760146368…68845048352604771841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.630 Γ— 10⁹⁡(96-digit number)
16309765958152029273…37690096705209543681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.261 Γ— 10⁹⁡(96-digit number)
32619531916304058547…75380193410419087361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.523 Γ— 10⁹⁡(96-digit number)
65239063832608117094…50760386820838174721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7
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 29680

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 92e2963fa591d998a75bf16af84ba70290c3adc9910c00e91022fd3dc7810461

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 #29,680 on Chainz β†—
Circulating Supply:57,736,993 XPMΒ·at block #6,811,609 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.
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