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Home/Chain Registry/Block #2,117,576

Block #2,117,576

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/15/2017, 2:57:00 PM Β· Difficulty 10.9061 Β· 4,724,226 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8f0935a987a049d471641e64a3b8da152dbe5a032a47bebd68e15190d5a86550
View on Chainz β†—

Difficulty

10.906126

Transactions

1

Size

243 B

Version

2

Bits

0ae7f7da

Nonce

226,686,303

Timestamp

5/15/2017, 2:57:00 PM

Confirmations

4,724,226

Merkle Root

2acba22956b9ee24969c8083b5f4c9407dc6fb2c694ed136bb1b3aa1e989800e
Transactions (1)
Coinbase2acba22956b9ee…1b3aa1e989800e
1 in β†’ 2 out8.3900 XPM152 B
AS57Lptt…gktTBHgtAXbk7f7A…Tx7JECPG
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.

2.482 Γ— 10⁹⁢(97-digit number)
24826166881647827098…14586200588933048320
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
2.482 Γ— 10⁹⁢(97-digit number)
24826166881647827098…14586200588933048319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.965 Γ— 10⁹⁢(97-digit number)
49652333763295654197…29172401177866096639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.930 Γ— 10⁹⁢(97-digit number)
99304667526591308394…58344802355732193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.986 Γ— 10⁹⁷(98-digit number)
19860933505318261678…16689604711464386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.972 Γ— 10⁹⁷(98-digit number)
39721867010636523357…33379209422928773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.944 Γ— 10⁹⁷(98-digit number)
79443734021273046715…66758418845857546239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.588 Γ— 10⁹⁸(99-digit number)
15888746804254609343…33516837691715092479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.177 Γ— 10⁹⁸(99-digit number)
31777493608509218686…67033675383430184959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.355 Γ— 10⁹⁸(99-digit number)
63554987217018437372…34067350766860369919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁹(100-digit number)
12710997443403687474…68134701533720739839
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 2117576

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 8f0935a987a049d471641e64a3b8da152dbe5a032a47bebd68e15190d5a86550

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 #2,117,576 on Chainz β†—
Circulating Supply:57,978,785 XPMΒ·at block #6,841,801 Β· updates every 60s
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