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Home/Chain Registry/Block #2,679,509

Block #2,679,509

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/27/2018, 1:45:18 AM Β· Difficulty 11.6927 Β· 4,162,324 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de25eb97aba1e904a8e9a0779419a211f24761e9530ec654c64c669c12e1d4b2
View on Chainz β†—

Difficulty

11.692674

Transactions

1

Size

200 B

Version

2

Bits

0bb15311

Nonce

1,228,564,588

Timestamp

5/27/2018, 1:45:18 AM

Confirmations

4,162,324

Merkle Root

d25710b555dd1813eacc6a83fe62d8dac8e8f33172a0d8a27376916b074a20c6
Transactions (1)
Coinbased25710b555dd18…76916b074a20c6
1 in β†’ 1 out7.3000 XPM110 B
AbnkqpWb…Hxknohpj
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.

3.216 Γ— 10⁹³(94-digit number)
32161561715806745279…60479170893922130520
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
3.216 Γ— 10⁹³(94-digit number)
32161561715806745279…60479170893922130519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.432 Γ— 10⁹³(94-digit number)
64323123431613490558…20958341787844261039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.286 Γ— 10⁹⁴(95-digit number)
12864624686322698111…41916683575688522079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.572 Γ— 10⁹⁴(95-digit number)
25729249372645396223…83833367151377044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.145 Γ— 10⁹⁴(95-digit number)
51458498745290792446…67666734302754088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.029 Γ— 10⁹⁡(96-digit number)
10291699749058158489…35333468605508176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.058 Γ— 10⁹⁡(96-digit number)
20583399498116316978…70666937211016353279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.116 Γ— 10⁹⁡(96-digit number)
41166798996232633957…41333874422032706559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.233 Γ— 10⁹⁡(96-digit number)
82333597992465267914…82667748844065413119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.646 Γ— 10⁹⁢(97-digit number)
16466719598493053582…65335497688130826239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.293 Γ— 10⁹⁢(97-digit number)
32933439196986107165…30670995376261652479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
6.586 Γ— 10⁹⁢(97-digit number)
65866878393972214331…61341990752523304959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2679509

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 de25eb97aba1e904a8e9a0779419a211f24761e9530ec654c64c669c12e1d4b2

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 #2,679,509 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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