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Home/Chain Registry/Block #2,276,808

Block #2,276,808

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2017, 9:23:16 PM Β· Difficulty 10.9551 Β· 4,566,851 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e537e9d56015502ee4bc42ccdf36bbf884271db684a97b2169755ec7a23d92a2
View on Chainz β†—

Difficulty

10.955068

Transactions

1

Size

199 B

Version

2

Bits

0af47f5d

Nonce

1,135,148,365

Timestamp

8/31/2017, 9:23:16 PM

Confirmations

4,566,851

Merkle Root

9a4d6b60ed590fa57fdbce1ed46c274d0bcc1d42503ac83d23b4b058f5386c16
Transactions (1)
Coinbase9a4d6b60ed590f…b4b058f5386c16
1 in β†’ 1 out8.3200 XPM110 B
AdLfUXkv…BSzbLTX2
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.

6.919 Γ— 10⁹²(93-digit number)
69194337566648237732…83663862302151318920
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
6.919 Γ— 10⁹²(93-digit number)
69194337566648237732…83663862302151318919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.383 Γ— 10⁹³(94-digit number)
13838867513329647546…67327724604302637839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.767 Γ— 10⁹³(94-digit number)
27677735026659295093…34655449208605275679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.535 Γ— 10⁹³(94-digit number)
55355470053318590186…69310898417210551359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁴(95-digit number)
11071094010663718037…38621796834421102719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.214 Γ— 10⁹⁴(95-digit number)
22142188021327436074…77243593668842205439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.428 Γ— 10⁹⁴(95-digit number)
44284376042654872149…54487187337684410879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.856 Γ— 10⁹⁴(95-digit number)
88568752085309744298…08974374675368821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.771 Γ— 10⁹⁡(96-digit number)
17713750417061948859…17948749350737643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.542 Γ— 10⁹⁡(96-digit number)
35427500834123897719…35897498701475287039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2276808

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 e537e9d56015502ee4bc42ccdf36bbf884271db684a97b2169755ec7a23d92a2

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 #2,276,808 on Chainz β†—
Circulating Supply:57,993,644 XPMΒ·at block #6,843,658 Β· updates every 60s
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