XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,075,070

Block #2,075,070

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2017, 10:17:27 PM Β· Difficulty 10.8401 Β· 4,751,801 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c2772cbf53a697eaf7e81e18068a67c13ad0a1cddf8fa40645ae942b5e36ac95
View on Chainz β†—

Difficulty

10.840125

Transactions

1

Size

199 B

Version

2

Bits

0ad71270

Nonce

224,648,192

Timestamp

4/17/2017, 10:17:27 PM

Confirmations

4,751,801

Merkle Root

c2b4dfa433ed80d872b58ff2957fc74df26ca0a4e11911c1eb45ed7571ecb4c6
Transactions (1)
Coinbasec2b4dfa433ed80…45ed7571ecb4c6
1 in β†’ 1 out8.5000 XPM109 B
ARRcCPyq…3UA7tFvm
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.

5.161 Γ— 10⁹⁡(96-digit number)
51610587741524809010…84743756851966593280
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.161 Γ— 10⁹⁡(96-digit number)
51610587741524809010…84743756851966593279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁢(97-digit number)
10322117548304961802…69487513703933186559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.064 Γ— 10⁹⁢(97-digit number)
20644235096609923604…38975027407866373119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.128 Γ— 10⁹⁢(97-digit number)
41288470193219847208…77950054815732746239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.257 Γ— 10⁹⁢(97-digit number)
82576940386439694417…55900109631465492479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.651 Γ— 10⁹⁷(98-digit number)
16515388077287938883…11800219262930984959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.303 Γ— 10⁹⁷(98-digit number)
33030776154575877766…23600438525861969919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.606 Γ— 10⁹⁷(98-digit number)
66061552309151755533…47200877051723939839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁸(99-digit number)
13212310461830351106…94401754103447879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.642 Γ— 10⁹⁸(99-digit number)
26424620923660702213…88803508206895759359
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2075070

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 c2772cbf53a697eaf7e81e18068a67c13ad0a1cddf8fa40645ae942b5e36ac95

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 #2,075,070 on Chainz β†—
Circulating Supply:57,859,131 XPMΒ·at block #6,826,870 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