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Home/Chain Registry/Block #2,098,604

Block #2,098,604

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2017, 6:13:12 PM Β· Difficulty 10.8628 Β· 4,732,927 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58ac69ebcf8cd2664ddd2766b3953cc5a48eadd34c4434fc1e2e2be093389c72
View on Chainz β†—

Difficulty

10.862750

Transactions

3

Size

2.48 KB

Version

2

Bits

0adcdd33

Nonce

811,258,973

Timestamp

5/3/2017, 6:13:12 PM

Confirmations

4,732,927

Merkle Root

7f40896f9886e9a7a150a0f47a60a9270853fe49d66dae9bc032693c068c74ec
Transactions (3)
Coinbase31b73b9b63d51d…aac6649363373b
1 in β†’ 1 out8.5000 XPM109 B
Abc6MEG8…5KnFnbSS
592be1f4a258e3…f396ea3e705802
8 in β†’ 2 out6590.4572 XPM1.23 KB
AJjTRjqF…9UT35ngjAQqE8W9M…N7Z7sQgo
13bdad3634160d…b50dac9d383ed3
7 in β†’ 1 out6910.4902 XPM1.05 KB
AYoy228q…feZqXfNq
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.

5.052 Γ— 10⁹⁡(96-digit number)
50525740743800942820…76489930738601707520
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
5.052 Γ— 10⁹⁡(96-digit number)
50525740743800942820…76489930738601707519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.010 Γ— 10⁹⁢(97-digit number)
10105148148760188564…52979861477203415039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.021 Γ— 10⁹⁢(97-digit number)
20210296297520377128…05959722954406830079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.042 Γ— 10⁹⁢(97-digit number)
40420592595040754256…11919445908813660159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.084 Γ— 10⁹⁢(97-digit number)
80841185190081508512…23838891817627320319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.616 Γ— 10⁹⁷(98-digit number)
16168237038016301702…47677783635254640639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.233 Γ— 10⁹⁷(98-digit number)
32336474076032603405…95355567270509281279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.467 Γ— 10⁹⁷(98-digit number)
64672948152065206810…90711134541018562559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.293 Γ— 10⁹⁸(99-digit number)
12934589630413041362…81422269082037125119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.586 Γ— 10⁹⁸(99-digit number)
25869179260826082724…62844538164074250239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.173 Γ— 10⁹⁸(99-digit number)
51738358521652165448…25689076328148500479
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 2098604

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 58ac69ebcf8cd2664ddd2766b3953cc5a48eadd34c4434fc1e2e2be093389c72

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 #2,098,604 on Chainz β†—
Circulating Supply:57,896,338 XPMΒ·at block #6,831,530 Β· updates every 60s
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