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Block #2,655,690

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2018, 9:39:49 AM Β· Difficulty 11.7032 Β· 4,186,603 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c0b072ffcbc8c776818666bfac26e2570f04a2b311fc28177aee6239f4b90866
View on Chainz β†—

Difficulty

11.703207

Transactions

3

Size

1.04 KB

Version

2

Bits

0bb40559

Nonce

497,932,778

Timestamp

5/10/2018, 9:39:49 AM

Confirmations

4,186,603

Merkle Root

1b628ecf573733431fbfc29a05bd3e22bbff32aa83ac50d1f388fa29d7870d30
Transactions (3)
Coinbasee2d5ad8387ed9e…48988e4a103264
1 in β†’ 1 out7.3100 XPM110 B
AGJppf8E…6FujkVV4
4660b4ea0e8a80…4058ac8d1eb645
2 in β†’ 1 out1001.9900 XPM340 B
AcwQfQHY…C2hkXuZ1
c849ec08412bef…63b41925dd3651
3 in β†’ 2 out740.0034 XPM523 B
AFpax2Bd…qyjtNUTJAZ5qaFx8…x8r4Jsi3
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.

7.648 Γ— 10⁹⁡(96-digit number)
76489283930209428760…06450902706700535680
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
7.648 Γ— 10⁹⁡(96-digit number)
76489283930209428760…06450902706700535679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.529 Γ— 10⁹⁢(97-digit number)
15297856786041885752…12901805413401071359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.059 Γ— 10⁹⁢(97-digit number)
30595713572083771504…25803610826802142719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.119 Γ— 10⁹⁢(97-digit number)
61191427144167543008…51607221653604285439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.223 Γ— 10⁹⁷(98-digit number)
12238285428833508601…03214443307208570879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.447 Γ— 10⁹⁷(98-digit number)
24476570857667017203…06428886614417141759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.895 Γ— 10⁹⁷(98-digit number)
48953141715334034406…12857773228834283519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.790 Γ— 10⁹⁷(98-digit number)
97906283430668068813…25715546457668567039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁸(99-digit number)
19581256686133613762…51431092915337134079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.916 Γ— 10⁹⁸(99-digit number)
39162513372267227525…02862185830674268159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.832 Γ— 10⁹⁸(99-digit number)
78325026744534455051…05724371661348536319
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 2655690

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 c0b072ffcbc8c776818666bfac26e2570f04a2b311fc28177aee6239f4b90866

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 #2,655,690 on Chainz β†—
Circulating Supply:57,982,748 XPMΒ·at block #6,842,292 Β· updates every 60s
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