XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #690,582

Block #690,582

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/24/2014, 11:06:58 AM Β· Difficulty 10.9547 Β· 6,105,920 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e043cd4b667b895077dbe5c8a6e90fd93aa016c3a7c325ba59240ea109878b6
View on Chainz β†—

Height

#690,582

Difficulty

10.954698

Transactions

2

Size

581 B

Version

2

Bits

0af46711

Nonce

44,900,906

Timestamp

8/24/2014, 11:06:58 AM

Confirmations

6,105,920

Merkle Root

5b2651b3ad9a0494681931dbd6f0691a0718199492b5cf632e0d5ad40030373c
Transactions (2)
Coinbase374dc04d90d0a9…f79383f9d19c28
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
67be59fba41293…c9440aa31fa37d
2 in β†’ 2 out1.0104 XPM374 B
AGDLtHhp…j2k1PJ17ATMTfKyf…nWX8yKJd
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.

1.692 Γ— 10⁹⁢(97-digit number)
16924256338181025257…14134360542440464640
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
1.692 Γ— 10⁹⁢(97-digit number)
16924256338181025257…14134360542440464639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.384 Γ— 10⁹⁢(97-digit number)
33848512676362050514…28268721084880929279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.769 Γ— 10⁹⁢(97-digit number)
67697025352724101028…56537442169761858559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.353 Γ— 10⁹⁷(98-digit number)
13539405070544820205…13074884339523717119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.707 Γ— 10⁹⁷(98-digit number)
27078810141089640411…26149768679047434239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.415 Γ— 10⁹⁷(98-digit number)
54157620282179280822…52299537358094868479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁸(99-digit number)
10831524056435856164…04599074716189736959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.166 Γ— 10⁹⁸(99-digit number)
21663048112871712329…09198149432379473919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.332 Γ— 10⁹⁸(99-digit number)
43326096225743424658…18396298864758947839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.665 Γ— 10⁹⁸(99-digit number)
86652192451486849316…36792597729517895679
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 690582

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 2e043cd4b667b895077dbe5c8a6e90fd93aa016c3a7c325ba59240ea109878b6

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 #690,582 on Chainz β†—
Circulating Supply:57,616,017 XPMΒ·at block #6,796,501 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