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Block #2,841,798

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/16/2018, 11:42:43 AM Β· Difficulty 11.7215 Β· 4,001,838 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e2e8c91c2af440665966938ef17e257ea0117ceac85475baab8fd4f2f228267d
View on Chainz β†—

Difficulty

11.721499

Transactions

1

Size

199 B

Version

2

Bits

0bb8b42d

Nonce

2,008,399,440

Timestamp

9/16/2018, 11:42:43 AM

Confirmations

4,001,838

Merkle Root

887c07a776101f7aed2f516b5e9955f4ec96507c2f6d77d0346adcb88d67b5a6
Transactions (1)
Coinbase887c07a776101f…6adcb88d67b5a6
1 in β†’ 1 out7.2700 XPM109 B
AQJFuMZW…awK3tUqT
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.

1.470 Γ— 10⁹⁴(95-digit number)
14702783113111878229…81362684308913477620
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
1.470 Γ— 10⁹⁴(95-digit number)
14702783113111878229…81362684308913477619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.940 Γ— 10⁹⁴(95-digit number)
29405566226223756459…62725368617826955239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.881 Γ— 10⁹⁴(95-digit number)
58811132452447512919…25450737235653910479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁡(96-digit number)
11762226490489502583…50901474471307820959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁡(96-digit number)
23524452980979005167…01802948942615641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.704 Γ— 10⁹⁡(96-digit number)
47048905961958010335…03605897885231283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.409 Γ— 10⁹⁡(96-digit number)
94097811923916020671…07211795770462567679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁢(97-digit number)
18819562384783204134…14423591540925135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.763 Γ— 10⁹⁢(97-digit number)
37639124769566408268…28847183081850270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.527 Γ— 10⁹⁢(97-digit number)
75278249539132816537…57694366163700541439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.505 Γ— 10⁹⁷(98-digit number)
15055649907826563307…15388732327401082879
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 2841798

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 e2e8c91c2af440665966938ef17e257ea0117ceac85475baab8fd4f2f228267d

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 #2,841,798 on Chainz β†—
Circulating Supply:57,993,456 XPMΒ·at block #6,843,635 Β· updates every 60s
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