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Home/Chain Registry/Block #2,855,606

Block #2,855,606

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2018, 8:47:44 AM Β· Difficulty 11.6981 Β· 3,976,924 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e715cf9f7d1583cccde45ff68347253ebdd0a15fa043b84b7bbcfd6a79791141
View on Chainz β†—

Difficulty

11.698104

Transactions

1

Size

200 B

Version

2

Bits

0bb2b6f5

Nonce

1,612,033,649

Timestamp

9/26/2018, 8:47:44 AM

Confirmations

3,976,924

Merkle Root

11286e2f3bc700cef11180912f248766ef04cda4ecc75b82cf7b494342ebcf7b
Transactions (1)
Coinbase11286e2f3bc700…7b494342ebcf7b
1 in β†’ 1 out7.3000 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.230 Γ— 10⁹⁴(95-digit number)
12308037496916154441…68682104604062439680
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
1.230 Γ— 10⁹⁴(95-digit number)
12308037496916154441…68682104604062439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.461 Γ— 10⁹⁴(95-digit number)
24616074993832308883…37364209208124879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.923 Γ— 10⁹⁴(95-digit number)
49232149987664617766…74728418416249758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.846 Γ— 10⁹⁴(95-digit number)
98464299975329235532…49456836832499517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.969 Γ— 10⁹⁡(96-digit number)
19692859995065847106…98913673664999034879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.938 Γ— 10⁹⁡(96-digit number)
39385719990131694213…97827347329998069759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.877 Γ— 10⁹⁡(96-digit number)
78771439980263388426…95654694659996139519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁢(97-digit number)
15754287996052677685…91309389319992279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.150 Γ— 10⁹⁢(97-digit number)
31508575992105355370…82618778639984558079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.301 Γ— 10⁹⁢(97-digit number)
63017151984210710741…65237557279969116159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁷(98-digit number)
12603430396842142148…30475114559938232319
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 2855606

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 e715cf9f7d1583cccde45ff68347253ebdd0a15fa043b84b7bbcfd6a79791141

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 #2,855,606 on Chainz β†—
Circulating Supply:57,904,400 XPMΒ·at block #6,832,529 Β· updates every 60s
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