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Home/Chain Registry/Block #2,780,296

Block #2,780,296

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2018, 1:14:04 PM Β· Difficulty 11.6504 Β· 4,052,679 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98246c21a959a6eb55acddfc5f505ceb3a684179e066960214af94b95f229ca3
View on Chainz β†—

Difficulty

11.650380

Transactions

1

Size

201 B

Version

2

Bits

0ba67f56

Nonce

779,944,395

Timestamp

8/5/2018, 1:14:04 PM

Confirmations

4,052,679

Merkle Root

baba85bf59b143a65a91c1efd2434991fdab193d46b6721786b27070ae7b631e
Transactions (1)
Coinbasebaba85bf59b143…b27070ae7b631e
1 in β†’ 1 out7.3600 XPM110 B
AJFgGrNb…ELUb7LqZ
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.

9.587 Γ— 10⁹⁡(96-digit number)
95872718622994042185…27251464183630481600
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
9.587 Γ— 10⁹⁡(96-digit number)
95872718622994042185…27251464183630481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.917 Γ— 10⁹⁢(97-digit number)
19174543724598808437…54502928367260963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.834 Γ— 10⁹⁢(97-digit number)
38349087449197616874…09005856734521926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.669 Γ— 10⁹⁢(97-digit number)
76698174898395233748…18011713469043852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁷(98-digit number)
15339634979679046749…36023426938087705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁷(98-digit number)
30679269959358093499…72046853876175411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁷(98-digit number)
61358539918716186998…44093707752350822399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁸(99-digit number)
12271707983743237399…88187415504701644799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁸(99-digit number)
24543415967486474799…76374831009403289599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁸(99-digit number)
49086831934972949599…52749662018806579199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.817 Γ— 10⁹⁸(99-digit number)
98173663869945899198…05499324037613158399
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 2780296

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 98246c21a959a6eb55acddfc5f505ceb3a684179e066960214af94b95f229ca3

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 #2,780,296 on Chainz β†—
Circulating Supply:57,907,978 XPMΒ·at block #6,832,974 Β· updates every 60s
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