XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #37,585

Block #37,585

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 10:51:21 AM Β· Difficulty 8.0467 Β· 6,769,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd86de4314ca4e891416269cf9bd1d37d2798ceb316bae8c26212538e447be47
View on Chainz β†—

Height

#37,585

Difficulty

8.046715

Transactions

1

Size

204 B

Version

2

Bits

080bf587

Nonce

301

Timestamp

7/14/2013, 10:51:21 AM

Confirmations

6,769,854

Merkle Root

c119d5432606b046d36ebede895204471d3b7323c4e0fb14a3b052f333dd66d4
Transactions (1)
Coinbasec119d5432606b0…b052f333dd66d4
1 in β†’ 1 out15.4200 XPM110 B
Ae7LsdbR…9nruBRWt
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.

3.828 Γ— 10¹⁰⁴(105-digit number)
38282002221616157847…73141306645829581360
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
3.828 Γ— 10¹⁰⁴(105-digit number)
38282002221616157847…73141306645829581359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.656 Γ— 10¹⁰⁴(105-digit number)
76564004443232315695…46282613291659162719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.531 Γ— 10¹⁰⁡(106-digit number)
15312800888646463139…92565226583318325439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.062 Γ— 10¹⁰⁡(106-digit number)
30625601777292926278…85130453166636650879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.125 Γ— 10¹⁰⁡(106-digit number)
61251203554585852556…70260906333273301759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.225 Γ— 10¹⁰⁢(107-digit number)
12250240710917170511…40521812666546603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.450 Γ— 10¹⁰⁢(107-digit number)
24500481421834341022…81043625333093207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.900 Γ— 10¹⁰⁢(107-digit number)
49000962843668682044…62087250666186414079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 37585

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 fd86de4314ca4e891416269cf9bd1d37d2798ceb316bae8c26212538e447be47

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 #37,585 on Chainz β†—
Circulating Supply:57,703,533 XPMΒ·at block #6,807,438 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