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Home/Chain Registry/Block #2,760,941

Block #2,760,941

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 1:50:36 AM Β· Difficulty 11.6530 Β· 4,082,850 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55e54905772c895a3bb5237756734edb5b133fd55632dc7be28c6b780ab3d688
View on Chainz β†—

Difficulty

11.652963

Transactions

1

Size

200 B

Version

2

Bits

0ba7288d

Nonce

1,837,869,313

Timestamp

7/23/2018, 1:50:36 AM

Confirmations

4,082,850

Merkle Root

accaf36df940443d24a37215dc4db11cff1e06a5049335630232fbe2f71fb566
Transactions (1)
Coinbaseaccaf36df94044…32fbe2f71fb566
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.670 Γ— 10⁹⁴(95-digit number)
86707947521581487617…68630555643338664840
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
8.670 Γ— 10⁹⁴(95-digit number)
86707947521581487617…68630555643338664839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁡(96-digit number)
17341589504316297523…37261111286677329679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.468 Γ— 10⁹⁡(96-digit number)
34683179008632595046…74522222573354659359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.936 Γ— 10⁹⁡(96-digit number)
69366358017265190093…49044445146709318719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁢(97-digit number)
13873271603453038018…98088890293418637439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.774 Γ— 10⁹⁢(97-digit number)
27746543206906076037…96177780586837274879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.549 Γ— 10⁹⁢(97-digit number)
55493086413812152074…92355561173674549759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁷(98-digit number)
11098617282762430414…84711122347349099519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.219 Γ— 10⁹⁷(98-digit number)
22197234565524860829…69422244694698199039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.439 Γ— 10⁹⁷(98-digit number)
44394469131049721659…38844489389396398079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.878 Γ— 10⁹⁷(98-digit number)
88788938262099443319…77688978778792796159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.775 Γ— 10⁹⁸(99-digit number)
17757787652419888663…55377957557585592319
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 2760941

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 55e54905772c895a3bb5237756734edb5b133fd55632dc7be28c6b780ab3d688

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 #2,760,941 on Chainz β†—
Circulating Supply:57,994,705 XPMΒ·at block #6,843,790 Β· updates every 60s
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