XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,139,610

Block #2,139,610

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2017, 8:28:19 PM Β· Difficulty 10.8785 Β· 4,699,641 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6949c23e07d876ff8262ffcb3b06cf1defe40f9c8aeb2f12c6265e22a1cc81a5
View on Chainz β†—

Difficulty

10.878483

Transactions

1

Size

201 B

Version

2

Bits

0ae0e443

Nonce

67,351,933

Timestamp

5/31/2017, 8:28:19 PM

Confirmations

4,699,641

Merkle Root

723110a9d807de256fc85138c9dff58200d14ade419d6b95cda6bf576dcab867
Transactions (1)
Coinbase723110a9d807de…a6bf576dcab867
1 in β†’ 1 out8.4400 XPM110 B
AGnbWLY4…RP2ZE4NW
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.

3.218 Γ— 10⁹⁢(97-digit number)
32180355864942727162…86596393895828807680
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
3.218 Γ— 10⁹⁢(97-digit number)
32180355864942727162…86596393895828807679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.436 Γ— 10⁹⁢(97-digit number)
64360711729885454325…73192787791657615359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.287 Γ— 10⁹⁷(98-digit number)
12872142345977090865…46385575583315230719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.574 Γ— 10⁹⁷(98-digit number)
25744284691954181730…92771151166630461439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.148 Γ— 10⁹⁷(98-digit number)
51488569383908363460…85542302333260922879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.029 Γ— 10⁹⁸(99-digit number)
10297713876781672692…71084604666521845759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.059 Γ— 10⁹⁸(99-digit number)
20595427753563345384…42169209333043691519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.119 Γ— 10⁹⁸(99-digit number)
41190855507126690768…84338418666087383039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.238 Γ— 10⁹⁸(99-digit number)
82381711014253381536…68676837332174766079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.647 Γ— 10⁹⁹(100-digit number)
16476342202850676307…37353674664349532159
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 2139610

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 6949c23e07d876ff8262ffcb3b06cf1defe40f9c8aeb2f12c6265e22a1cc81a5

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 #2,139,610 on Chainz β†—
Circulating Supply:57,958,291 XPMΒ·at block #6,839,250 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