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Home/Chain Registry/Block #2,268,646

Block #2,268,646

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2017, 9:33:22 AM Β· Difficulty 10.9525 Β· 4,568,091 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cb7bdb4445448a272d01b6b05166b7f0692252d9859c544dee7677d928a2a6f9
View on Chainz β†—

Difficulty

10.952513

Transactions

1

Size

199 B

Version

2

Bits

0af3d7e2

Nonce

970,482,444

Timestamp

8/26/2017, 9:33:22 AM

Confirmations

4,568,091

Merkle Root

021a18326951fc7ae51a3dd8c28b6baca1249ba4a6c4281c18af3c4a6ace1fe7
Transactions (1)
Coinbase021a18326951fc…af3c4a6ace1fe7
1 in β†’ 1 out8.3200 XPM109 B
AascrrMB…TKuMght2
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.

1.882 Γ— 10⁹⁴(95-digit number)
18822056901486641409…54852712150770207360
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
1.882 Γ— 10⁹⁴(95-digit number)
18822056901486641409…54852712150770207359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.764 Γ— 10⁹⁴(95-digit number)
37644113802973282819…09705424301540414719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.528 Γ— 10⁹⁴(95-digit number)
75288227605946565638…19410848603080829439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.505 Γ— 10⁹⁡(96-digit number)
15057645521189313127…38821697206161658879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.011 Γ— 10⁹⁡(96-digit number)
30115291042378626255…77643394412323317759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.023 Γ— 10⁹⁡(96-digit number)
60230582084757252510…55286788824646635519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.204 Γ— 10⁹⁢(97-digit number)
12046116416951450502…10573577649293271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.409 Γ— 10⁹⁢(97-digit number)
24092232833902901004…21147155298586542079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.818 Γ— 10⁹⁢(97-digit number)
48184465667805802008…42294310597173084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.636 Γ— 10⁹⁢(97-digit number)
96368931335611604017…84588621194346168319
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 2268646

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 cb7bdb4445448a272d01b6b05166b7f0692252d9859c544dee7677d928a2a6f9

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 #2,268,646 on Chainz β†—
Circulating Supply:57,938,179 XPMΒ·at block #6,836,736 Β· updates every 60s
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