XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #528,251

Block #528,251

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2014, 1:11:15 PM Β· Difficulty 10.8862 Β· 6,272,300 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4342e7928010bd7b636258d14d5193418e45cb2a7cbcacfc45f4af023b010531
View on Chainz β†—

Height

#528,251

Difficulty

10.886159

Transactions

1

Size

208 B

Version

2

Bits

0ae2db4e

Nonce

3,736,537

Timestamp

5/6/2014, 1:11:15 PM

Confirmations

6,272,300

Merkle Root

eb8b39368bc264e9c7b2cfb41127b3d07b253d9ad6acae8684b2f4c7890fbb3d
Transactions (1)
Coinbaseeb8b39368bc264…b2f4c7890fbb3d
1 in β†’ 1 out8.4200 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.

2.309 Γ— 10¹⁰⁰(101-digit number)
23091055557512613888…98018549096376391680
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
2.309 Γ— 10¹⁰⁰(101-digit number)
23091055557512613888…98018549096376391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.618 Γ— 10¹⁰⁰(101-digit number)
46182111115025227777…96037098192752783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.236 Γ— 10¹⁰⁰(101-digit number)
92364222230050455555…92074196385505566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.847 Γ— 10¹⁰¹(102-digit number)
18472844446010091111…84148392771011133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.694 Γ— 10¹⁰¹(102-digit number)
36945688892020182222…68296785542022266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.389 Γ— 10¹⁰¹(102-digit number)
73891377784040364444…36593571084044533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.477 Γ— 10¹⁰²(103-digit number)
14778275556808072888…73187142168089067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.955 Γ— 10¹⁰²(103-digit number)
29556551113616145777…46374284336178135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.911 Γ— 10¹⁰²(103-digit number)
59113102227232291555…92748568672356270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.182 Γ— 10¹⁰³(104-digit number)
11822620445446458311…85497137344712540159
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 528251

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 4342e7928010bd7b636258d14d5193418e45cb2a7cbcacfc45f4af023b010531

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 #528,251 on Chainz β†—
Circulating Supply:57,648,472 XPMΒ·at block #6,800,550 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