XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,639,904

Block #2,639,904

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 7:48:02 PM Β· Difficulty 11.5581 Β· 4,193,838 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
025efcb529425ad907e6ed06924b16d45003fb9ee05b859f1c6a9ac8ec71a563
View on Chainz β†—

Difficulty

11.558128

Transactions

1

Size

200 B

Version

2

Bits

0b8ee17c

Nonce

57,565,308

Timestamp

4/30/2018, 7:48:02 PM

Confirmations

4,193,838

Merkle Root

55fc12346661c11092ed51363278429edb55f999bca565664c29522dd203cc7a
Transactions (1)
Coinbase55fc12346661c1…29522dd203cc7a
1 in β†’ 1 out7.4700 XPM109 B
AZgSSij5…TY6avU9W
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.

3.119 Γ— 10⁹⁢(97-digit number)
31199876743048357959…87975622118699304960
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
3.119 Γ— 10⁹⁢(97-digit number)
31199876743048357959…87975622118699304959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.239 Γ— 10⁹⁢(97-digit number)
62399753486096715918…75951244237398609919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.247 Γ— 10⁹⁷(98-digit number)
12479950697219343183…51902488474797219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.495 Γ— 10⁹⁷(98-digit number)
24959901394438686367…03804976949594439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.991 Γ— 10⁹⁷(98-digit number)
49919802788877372734…07609953899188879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.983 Γ— 10⁹⁷(98-digit number)
99839605577754745469…15219907798377758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.996 Γ— 10⁹⁸(99-digit number)
19967921115550949093…30439815596755517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.993 Γ— 10⁹⁸(99-digit number)
39935842231101898187…60879631193511034879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.987 Γ— 10⁹⁸(99-digit number)
79871684462203796375…21759262387022069759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.597 Γ— 10⁹⁹(100-digit number)
15974336892440759275…43518524774044139519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.194 Γ— 10⁹⁹(100-digit number)
31948673784881518550…87037049548088279039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2639904

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 025efcb529425ad907e6ed06924b16d45003fb9ee05b859f1c6a9ac8ec71a563

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 #2,639,904 on Chainz β†—
Circulating Supply:57,914,154 XPMΒ·at block #6,833,741 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