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Home/Chain Registry/Block #2,278,695

Block #2,278,695

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2017, 3:43:09 AM Β· Difficulty 10.9557 Β· 4,552,312 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
462b987429a0e630805402d62e9114cbcb9e90ccb3752cf7b073a25c65eff2a6
View on Chainz β†—

Difficulty

10.955719

Transactions

2

Size

424 B

Version

2

Bits

0af4aa04

Nonce

704,954,073

Timestamp

9/2/2017, 3:43:09 AM

Confirmations

4,552,312

Merkle Root

6df548f82b0ed6c7c85281e22d13f232c14f05487ac9e0c375b1eac9c3e3c9c4
Transactions (2)
Coinbase178454fbdf4650…375f530aea45ac
1 in β†’ 1 out8.3300 XPM110 B
AX2Avm4x…bWrXRa1F
3ef09203861642…c4bc1a950cfc42
1 in β†’ 2 out1287.8841 XPM225 B
AHadFj5Z…M51Cch7FAS8Swa5k…emSJQqiE
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.

1.494 Γ— 10⁹²(93-digit number)
14946273656899672682…24775372671586052570
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
1.494 Γ— 10⁹²(93-digit number)
14946273656899672682…24775372671586052569
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.989 Γ— 10⁹²(93-digit number)
29892547313799345365…49550745343172105139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.978 Γ— 10⁹²(93-digit number)
59785094627598690731…99101490686344210279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.195 Γ— 10⁹³(94-digit number)
11957018925519738146…98202981372688420559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.391 Γ— 10⁹³(94-digit number)
23914037851039476292…96405962745376841119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.782 Γ— 10⁹³(94-digit number)
47828075702078952585…92811925490753682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.565 Γ— 10⁹³(94-digit number)
95656151404157905171…85623850981507364479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.913 Γ— 10⁹⁴(95-digit number)
19131230280831581034…71247701963014728959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.826 Γ— 10⁹⁴(95-digit number)
38262460561663162068…42495403926029457919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.652 Γ— 10⁹⁴(95-digit number)
76524921123326324136…84990807852058915839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁡(96-digit number)
15304984224665264827…69981615704117831679
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 2278695

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 462b987429a0e630805402d62e9114cbcb9e90ccb3752cf7b073a25c65eff2a6

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 #2,278,695 on Chainz β†—
Circulating Supply:57,892,198 XPMΒ·at block #6,831,006 Β· updates every 60s
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