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Home/Chain Registry/Block #2,257,326

Block #2,257,326

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2017, 1:47:02 PM Β· Difficulty 10.9517 Β· 4,585,617 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d653f8167d139cdd3e7f64ac00fffdd8456b49ed956f2036e05a2f4a7ea8d6e
View on Chainz β†—

Difficulty

10.951657

Transactions

1

Size

201 B

Version

2

Bits

0af39fcb

Nonce

1,724,825,984

Timestamp

8/18/2017, 1:47:02 PM

Confirmations

4,585,617

Merkle Root

03eca98b942f53eb0f77962dd42a70748cb9ddc9cd7ddc4a505b2a20d17ecc27
Transactions (1)
Coinbase03eca98b942f53…5b2a20d17ecc27
1 in β†’ 1 out8.3200 XPM110 B
ATGGcSEh…4Jn4mqvf
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.

3.117 Γ— 10⁹⁢(97-digit number)
31171056717019136870…42562482175702343680
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.117 Γ— 10⁹⁢(97-digit number)
31171056717019136870…42562482175702343681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.234 Γ— 10⁹⁢(97-digit number)
62342113434038273741…85124964351404687361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.246 Γ— 10⁹⁷(98-digit number)
12468422686807654748…70249928702809374721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.493 Γ— 10⁹⁷(98-digit number)
24936845373615309496…40499857405618749441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.987 Γ— 10⁹⁷(98-digit number)
49873690747230618993…80999714811237498881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.974 Γ— 10⁹⁷(98-digit number)
99747381494461237986…61999429622474997761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.994 Γ— 10⁹⁸(99-digit number)
19949476298892247597…23998859244949995521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.989 Γ— 10⁹⁸(99-digit number)
39898952597784495194…47997718489899991041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.979 Γ— 10⁹⁸(99-digit number)
79797905195568990389…95995436979799982081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.595 Γ— 10⁹⁹(100-digit number)
15959581039113798077…91990873959599964161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.191 Γ— 10⁹⁹(100-digit number)
31919162078227596155…83981747919199928321
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2257326

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 0d653f8167d139cdd3e7f64ac00fffdd8456b49ed956f2036e05a2f4a7ea8d6e

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 #2,257,326 on Chainz β†—
Circulating Supply:57,987,894 XPMΒ·at block #6,842,942 Β· updates every 60s
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