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Home/Chain Registry/Block #2,072,259

Block #2,072,259

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/15/2017, 4:04:24 PM Β· Difficulty 10.8534 Β· 4,770,579 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be5fb4dec82fa3c3b09c0a52c6a88b90c4870b9de2e18495fe886fe5d98e9d60
View on Chainz β†—

Difficulty

10.853445

Transactions

1

Size

199 B

Version

2

Bits

0ada7b5b

Nonce

960,668,434

Timestamp

4/15/2017, 4:04:24 PM

Confirmations

4,770,579

Merkle Root

4ef3b6e10d742453734a22d8284fc7089fe357faf5468434346e287d581f553f
Transactions (1)
Coinbase4ef3b6e10d7424…6e287d581f553f
1 in β†’ 1 out8.4800 XPM110 B
ARiFoUGp…EMySuvwZ
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.

8.311 Γ— 10⁹²(93-digit number)
83112825872029585754…20900030008617420800
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
8.311 Γ— 10⁹²(93-digit number)
83112825872029585754…20900030008617420799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.662 Γ— 10⁹³(94-digit number)
16622565174405917150…41800060017234841599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.324 Γ— 10⁹³(94-digit number)
33245130348811834301…83600120034469683199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.649 Γ— 10⁹³(94-digit number)
66490260697623668603…67200240068939366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁴(95-digit number)
13298052139524733720…34400480137878732799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.659 Γ— 10⁹⁴(95-digit number)
26596104279049467441…68800960275757465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.319 Γ— 10⁹⁴(95-digit number)
53192208558098934882…37601920551514931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁡(96-digit number)
10638441711619786976…75203841103029862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁡(96-digit number)
21276883423239573953…50407682206059724799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.255 Γ— 10⁹⁡(96-digit number)
42553766846479147906…00815364412119449599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.510 Γ— 10⁹⁡(96-digit number)
85107533692958295812…01630728824238899199
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 2072259

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 be5fb4dec82fa3c3b09c0a52c6a88b90c4870b9de2e18495fe886fe5d98e9d60

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 #2,072,259 on Chainz β†—
Circulating Supply:57,987,047 XPMΒ·at block #6,842,837 Β· updates every 60s
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