XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,095,365

Block #2,095,365

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2017, 5:57:15 AM Β· Difficulty 10.8725 Β· 4,744,688 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb7f0ae4b819a074b0e89bb8a97b7ea36eb65262cf77195d31e9ce0c7562aff4
View on Chainz β†—

Difficulty

10.872532

Transactions

1

Size

199 B

Version

2

Bits

0adf5e3a

Nonce

1,154,514,347

Timestamp

5/1/2017, 5:57:15 AM

Confirmations

4,744,688

Merkle Root

1aaac912de1d61bc48762f5363e946496acaeaa55aa6f0978b9f1f32074cb773
Transactions (1)
Coinbase1aaac912de1d61…9f1f32074cb773
1 in β†’ 1 out8.4500 XPM109 B
AYCPfgJD…WD9w4Pgh
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.

2.644 Γ— 10⁹⁡(96-digit number)
26440456050719038608…44154224619901488000
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
2.644 Γ— 10⁹⁡(96-digit number)
26440456050719038608…44154224619901488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.288 Γ— 10⁹⁡(96-digit number)
52880912101438077217…88308449239802976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10576182420287615443…76616898479605952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21152364840575230886…53233796959211904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.230 Γ— 10⁹⁢(97-digit number)
42304729681150461773…06467593918423808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.460 Γ— 10⁹⁢(97-digit number)
84609459362300923547…12935187836847616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.692 Γ— 10⁹⁷(98-digit number)
16921891872460184709…25870375673695232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.384 Γ— 10⁹⁷(98-digit number)
33843783744920369418…51740751347390464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.768 Γ— 10⁹⁷(98-digit number)
67687567489840738837…03481502694780928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.353 Γ— 10⁹⁸(99-digit number)
13537513497968147767…06963005389561856001
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 2095365

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 eb7f0ae4b819a074b0e89bb8a97b7ea36eb65262cf77195d31e9ce0c7562aff4

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 #2,095,365 on Chainz β†—
Circulating Supply:57,964,733 XPMΒ·at block #6,840,052 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