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Home/Chain Registry/Block #2,694,986

Block #2,694,986

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/7/2018, 12:00:43 AM Β· Difficulty 11.6774 Β· 4,143,931 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f35f343ac0abfaba381bd3a5d89f64789b4777e44c589e401e9c6609ab97d272
View on Chainz β†—

Difficulty

11.677350

Transactions

2

Size

868 B

Version

2

Bits

0bad66d5

Nonce

75,111,211

Timestamp

6/7/2018, 12:00:43 AM

Confirmations

4,143,931

Merkle Root

ee5cb49ca996e97d5c3f0ffb022d4b7ef5627c15dfabeccf22098a395c507887
Transactions (2)
Coinbase95927479c902d0…817c7ed522161f
1 in β†’ 1 out7.3300 XPM110 B
AbU1Ku7S…L9XXumvw
658aea0f26b01f…31fc469f414932
4 in β†’ 2 out8000.0099 XPM668 B
AH3A2GJU…NLYdkucbAMoua8nu…E2ritVsD
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.

1.904 Γ— 10⁹⁡(96-digit number)
19042688925033041433…31655035753631426560
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.904 Γ— 10⁹⁡(96-digit number)
19042688925033041433…31655035753631426561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.808 Γ— 10⁹⁡(96-digit number)
38085377850066082867…63310071507262853121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.617 Γ— 10⁹⁡(96-digit number)
76170755700132165735…26620143014525706241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.523 Γ— 10⁹⁢(97-digit number)
15234151140026433147…53240286029051412481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.046 Γ— 10⁹⁢(97-digit number)
30468302280052866294…06480572058102824961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.093 Γ— 10⁹⁢(97-digit number)
60936604560105732588…12961144116205649921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.218 Γ— 10⁹⁷(98-digit number)
12187320912021146517…25922288232411299841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.437 Γ— 10⁹⁷(98-digit number)
24374641824042293035…51844576464822599681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.874 Γ— 10⁹⁷(98-digit number)
48749283648084586070…03689152929645199361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.749 Γ— 10⁹⁷(98-digit number)
97498567296169172141…07378305859290398721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.949 Γ— 10⁹⁸(99-digit number)
19499713459233834428…14756611718580797441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.899 Γ— 10⁹⁸(99-digit number)
38999426918467668856…29513223437161594881
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2694986

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 f35f343ac0abfaba381bd3a5d89f64789b4777e44c589e401e9c6609ab97d272

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 #2,694,986 on Chainz β†—
Circulating Supply:57,955,597 XPMΒ·at block #6,838,916 Β· updates every 60s
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