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Home/Chain Registry/Block #2,260,500

Block #2,260,500

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2017, 6:37:16 PM Β· Difficulty 10.9518 Β· 4,573,474 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb046a773992b3734a94a470b334aa297115305bea2d1e62fa7e98e8136d3e2b
View on Chainz β†—

Difficulty

10.951811

Transactions

2

Size

427 B

Version

2

Bits

0af3a9e9

Nonce

285,168,044

Timestamp

8/20/2017, 6:37:16 PM

Confirmations

4,573,474

Merkle Root

613bb0fc7abc3863e2de3b9c5c7dfe5230a19b998bdcc8b347c6acba39412fa9
Transactions (2)
Coinbase47c4fe36993a6f…d006644b52501b
1 in β†’ 1 out8.3800 XPM110 B
AMG79Uq8…4vcWt49M
e0e4dc75b7bfc3…63a636061a80d1
1 in β†’ 2 out987.9600 XPM227 B
AammHJuN…yaRcHuV7ANVP32Cy…syvqoZVG
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.

2.926 Γ— 10⁹⁡(96-digit number)
29261235131582555184…50798555113717455360
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
2.926 Γ— 10⁹⁡(96-digit number)
29261235131582555184…50798555113717455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.852 Γ— 10⁹⁡(96-digit number)
58522470263165110368…01597110227434910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.170 Γ— 10⁹⁢(97-digit number)
11704494052633022073…03194220454869821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.340 Γ— 10⁹⁢(97-digit number)
23408988105266044147…06388440909739642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.681 Γ— 10⁹⁢(97-digit number)
46817976210532088294…12776881819479285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.363 Γ— 10⁹⁢(97-digit number)
93635952421064176589…25553763638958571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.872 Γ— 10⁹⁷(98-digit number)
18727190484212835317…51107527277917143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.745 Γ— 10⁹⁷(98-digit number)
37454380968425670635…02215054555834286081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.490 Γ— 10⁹⁷(98-digit number)
74908761936851341271…04430109111668572161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.498 Γ— 10⁹⁸(99-digit number)
14981752387370268254…08860218223337144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.996 Γ— 10⁹⁸(99-digit number)
29963504774740536508…17720436446674288641
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 2260500

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 eb046a773992b3734a94a470b334aa297115305bea2d1e62fa7e98e8136d3e2b

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 #2,260,500 on Chainz β†—
Circulating Supply:57,916,015 XPMΒ·at block #6,833,973 Β· updates every 60s
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