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Home/Chain Registry/Block #2,831,634

Block #2,831,634

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2018, 11:25:09 AM Β· Difficulty 11.7175 Β· 4,007,342 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6e65273ee978ed64ca4b163a009415ffe18c4c109f1450b37c82655a7e768412
View on Chainz β†—

Difficulty

11.717452

Transactions

1

Size

200 B

Version

2

Bits

0bb7aaee

Nonce

772,522,549

Timestamp

9/9/2018, 11:25:09 AM

Confirmations

4,007,342

Merkle Root

5582cdc60e898a02602dc669717ce4b5d53c7ff619a5dd3c7119f55e13c60409
Transactions (1)
Coinbase5582cdc60e898a…19f55e13c60409
1 in β†’ 1 out7.2700 XPM110 B
ARJy4txq…G5jj8wC8
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.

5.716 Γ— 10⁹⁡(96-digit number)
57168826803363678784…13174762659187757440
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
5.716 Γ— 10⁹⁡(96-digit number)
57168826803363678784…13174762659187757439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁢(97-digit number)
11433765360672735756…26349525318375514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.286 Γ— 10⁹⁢(97-digit number)
22867530721345471513…52699050636751029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.573 Γ— 10⁹⁢(97-digit number)
45735061442690943027…05398101273502059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.147 Γ— 10⁹⁢(97-digit number)
91470122885381886055…10796202547004119039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.829 Γ— 10⁹⁷(98-digit number)
18294024577076377211…21592405094008238079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.658 Γ— 10⁹⁷(98-digit number)
36588049154152754422…43184810188016476159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.317 Γ— 10⁹⁷(98-digit number)
73176098308305508844…86369620376032952319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.463 Γ— 10⁹⁸(99-digit number)
14635219661661101768…72739240752065904639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.927 Γ— 10⁹⁸(99-digit number)
29270439323322203537…45478481504131809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.854 Γ— 10⁹⁸(99-digit number)
58540878646644407075…90956963008263618559
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 2831634

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 6e65273ee978ed64ca4b163a009415ffe18c4c109f1450b37c82655a7e768412

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 #2,831,634 on Chainz β†—
Circulating Supply:57,956,078 XPMΒ·at block #6,838,975 Β· updates every 60s
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