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Home/Chain Registry/Block #2,061,584

Block #2,061,584

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/8/2017, 2:52:53 AM Β· Difficulty 10.8587 Β· 4,783,161 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
875c80b4a34c2c1fb977355c89c9993a38e30b5ea84cf4fbe7b619637f8cf251
View on Chainz β†—

Difficulty

10.858692

Transactions

1

Size

199 B

Version

2

Bits

0adbd33d

Nonce

111,803,694

Timestamp

4/8/2017, 2:52:53 AM

Confirmations

4,783,161

Merkle Root

478f864c622987d74e3c84cc734e9ca923ccaab9f16d346fb390defecac19d4f
Transactions (1)
Coinbase478f864c622987…90defecac19d4f
1 in β†’ 1 out8.4700 XPM109 B
AQmJ3VeJ…U1zLrmvh
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.

6.678 Γ— 10⁹⁡(96-digit number)
66788495214899978557…12296712140284566720
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
6.678 Γ— 10⁹⁡(96-digit number)
66788495214899978557…12296712140284566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.335 Γ— 10⁹⁢(97-digit number)
13357699042979995711…24593424280569133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.671 Γ— 10⁹⁢(97-digit number)
26715398085959991423…49186848561138266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.343 Γ— 10⁹⁢(97-digit number)
53430796171919982846…98373697122276533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.068 Γ— 10⁹⁷(98-digit number)
10686159234383996569…96747394244553067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.137 Γ— 10⁹⁷(98-digit number)
21372318468767993138…93494788489106135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.274 Γ— 10⁹⁷(98-digit number)
42744636937535986277…86989576978212270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.548 Γ— 10⁹⁷(98-digit number)
85489273875071972554…73979153956424540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.709 Γ— 10⁹⁸(99-digit number)
17097854775014394510…47958307912849080319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.419 Γ— 10⁹⁸(99-digit number)
34195709550028789021…95916615825698160639
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 2061584

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 875c80b4a34c2c1fb977355c89c9993a38e30b5ea84cf4fbe7b619637f8cf251

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 #2,061,584 on Chainz β†—
Circulating Supply:58,002,373 XPMΒ·at block #6,844,744 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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