XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #726,845

Block #726,845

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2014, 4:36:21 AM Β· Difficulty 10.9612 Β· 6,068,762 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23f54b8610c26c8fe45a5aac54cc7b9e8a9629457c12c92cf57b77830a2d7aaf
View on Chainz β†—

Height

#726,845

Difficulty

10.961237

Transactions

1

Size

206 B

Version

2

Bits

0af6139e

Nonce

2,224,760,083

Timestamp

9/18/2014, 4:36:21 AM

Confirmations

6,068,762

Merkle Root

b62ab2ff54625b4a24bfdf1323abf9890f1cf5f39e85d1e049e31f87314dd13b
Transactions (1)
Coinbaseb62ab2ff54625b…e31f87314dd13b
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.797 Γ— 10⁹⁴(95-digit number)
37977001970588613509…62579528653956156880
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
3.797 Γ— 10⁹⁴(95-digit number)
37977001970588613509…62579528653956156881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.595 Γ— 10⁹⁴(95-digit number)
75954003941177227019…25159057307912313761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.519 Γ— 10⁹⁡(96-digit number)
15190800788235445403…50318114615824627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.038 Γ— 10⁹⁡(96-digit number)
30381601576470890807…00636229231649255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.076 Γ— 10⁹⁡(96-digit number)
60763203152941781615…01272458463298510081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.215 Γ— 10⁹⁢(97-digit number)
12152640630588356323…02544916926597020161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.430 Γ— 10⁹⁢(97-digit number)
24305281261176712646…05089833853194040321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.861 Γ— 10⁹⁢(97-digit number)
48610562522353425292…10179667706388080641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.722 Γ— 10⁹⁢(97-digit number)
97221125044706850584…20359335412776161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.944 Γ— 10⁹⁷(98-digit number)
19444225008941370116…40718670825552322561
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 726845

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 23f54b8610c26c8fe45a5aac54cc7b9e8a9629457c12c92cf57b77830a2d7aaf

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 #726,845 on Chainz β†—
Circulating Supply:57,608,920 XPMΒ·at block #6,795,606 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