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Home/Chain Registry/Block #2,257,796

Block #2,257,796

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2017, 8:55:32 PM Β· Difficulty 10.9521 Β· 4,585,484 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bee30b6609bc1e5b0915e6c4633e0cfe7398891594700e502db3d17b0e6156f2
View on Chainz β†—

Difficulty

10.952067

Transactions

1

Size

200 B

Version

2

Bits

0af3baaa

Nonce

1,871,471,684

Timestamp

8/18/2017, 8:55:32 PM

Confirmations

4,585,484

Merkle Root

329dd35efe01030476fe2cd798891bcdea4145598e626c1718a141dd8c8b27f9
Transactions (1)
Coinbase329dd35efe0103…a141dd8c8b27f9
1 in β†’ 1 out8.3200 XPM110 B
AP69kFXz…5ijmS8jd
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.

9.730 Γ— 10⁹⁴(95-digit number)
97301511237970637736…34438936824791558080
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
9.730 Γ— 10⁹⁴(95-digit number)
97301511237970637736…34438936824791558081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.946 Γ— 10⁹⁡(96-digit number)
19460302247594127547…68877873649583116161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.892 Γ— 10⁹⁡(96-digit number)
38920604495188255094…37755747299166232321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.784 Γ— 10⁹⁡(96-digit number)
77841208990376510189…75511494598332464641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.556 Γ— 10⁹⁢(97-digit number)
15568241798075302037…51022989196664929281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.113 Γ— 10⁹⁢(97-digit number)
31136483596150604075…02045978393329858561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.227 Γ— 10⁹⁢(97-digit number)
62272967192301208151…04091956786659717121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12454593438460241630…08183913573319434241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.490 Γ— 10⁹⁷(98-digit number)
24909186876920483260…16367827146638868481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.981 Γ— 10⁹⁷(98-digit number)
49818373753840966521…32735654293277736961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.963 Γ— 10⁹⁷(98-digit number)
99636747507681933042…65471308586555473921
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 2257796

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 bee30b6609bc1e5b0915e6c4633e0cfe7398891594700e502db3d17b0e6156f2

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 #2,257,796 on Chainz β†—
Circulating Supply:57,990,616 XPMΒ·at block #6,843,279 Β· updates every 60s
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