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Home/Chain Registry/Block #2,765,798

Block #2,765,798

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/26/2018, 7:28:23 AM Β· Difficulty 11.6666 Β· 4,073,586 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
adbef2dfc90adc02da62a9cbd0bc2e83811dc7332383a645b5f5cebefa6520b0
View on Chainz β†—

Difficulty

11.666649

Transactions

1

Size

200 B

Version

2

Bits

0baaa986

Nonce

83,506,471

Timestamp

7/26/2018, 7:28:23 AM

Confirmations

4,073,586

Merkle Root

59c85d686fccc822278e302dbab44913661c67155120fda408123d29d13e552d
Transactions (1)
Coinbase59c85d686fccc8…123d29d13e552d
1 in β†’ 1 out7.3300 XPM110 B
AHsmvWjW…DPmVQwMo
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.

2.298 Γ— 10⁹⁴(95-digit number)
22987732539419643051…79050520320609762000
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
2.298 Γ— 10⁹⁴(95-digit number)
22987732539419643051…79050520320609761999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.597 Γ— 10⁹⁴(95-digit number)
45975465078839286103…58101040641219523999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.195 Γ— 10⁹⁴(95-digit number)
91950930157678572207…16202081282439047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.839 Γ— 10⁹⁡(96-digit number)
18390186031535714441…32404162564878095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.678 Γ— 10⁹⁡(96-digit number)
36780372063071428883…64808325129756191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.356 Γ— 10⁹⁡(96-digit number)
73560744126142857766…29616650259512383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.471 Γ— 10⁹⁢(97-digit number)
14712148825228571553…59233300519024767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.942 Γ— 10⁹⁢(97-digit number)
29424297650457143106…18466601038049535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.884 Γ— 10⁹⁢(97-digit number)
58848595300914286212…36933202076099071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁷(98-digit number)
11769719060182857242…73866404152198143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.353 Γ— 10⁹⁷(98-digit number)
23539438120365714485…47732808304396287999
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 2765798

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 adbef2dfc90adc02da62a9cbd0bc2e83811dc7332383a645b5f5cebefa6520b0

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 #2,765,798 on Chainz β†—
Circulating Supply:57,959,355 XPMΒ·at block #6,839,383 Β· updates every 60s
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