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Home/Chain Registry/Block #2,927,857

Block #2,927,857

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2018, 3:22:55 AM Β· Difficulty 11.3695 Β· 3,913,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
95c769bc3e8a0208f17d3a02ace1cf9c81eee29912bf094a0ceabcba189e4a1d
View on Chainz β†—

Difficulty

11.369546

Transactions

1

Size

200 B

Version

2

Bits

0b5e9a94

Nonce

1,549,445,244

Timestamp

11/18/2018, 3:22:55 AM

Confirmations

3,913,593

Merkle Root

26c996df70ba4d5c45c92b2332b5c1f976c2ca339985bc4fa24281482a0b4976
Transactions (1)
Coinbase26c996df70ba4d…4281482a0b4976
1 in β†’ 1 out7.7200 XPM110 B
AUhjokok…k5m93PZR
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.

2.653 Γ— 10⁹⁴(95-digit number)
26531064381184949671…28796503400235077080
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
2.653 Γ— 10⁹⁴(95-digit number)
26531064381184949671…28796503400235077081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.306 Γ— 10⁹⁴(95-digit number)
53062128762369899343…57593006800470154161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.061 Γ— 10⁹⁡(96-digit number)
10612425752473979868…15186013600940308321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.122 Γ— 10⁹⁡(96-digit number)
21224851504947959737…30372027201880616641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.244 Γ— 10⁹⁡(96-digit number)
42449703009895919474…60744054403761233281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.489 Γ— 10⁹⁡(96-digit number)
84899406019791838949…21488108807522466561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.697 Γ— 10⁹⁢(97-digit number)
16979881203958367789…42976217615044933121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.395 Γ— 10⁹⁢(97-digit number)
33959762407916735579…85952435230089866241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.791 Γ— 10⁹⁢(97-digit number)
67919524815833471159…71904870460179732481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.358 Γ— 10⁹⁷(98-digit number)
13583904963166694231…43809740920359464961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.716 Γ— 10⁹⁷(98-digit number)
27167809926333388463…87619481840718929921
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 2927857

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 95c769bc3e8a0208f17d3a02ace1cf9c81eee29912bf094a0ceabcba189e4a1d

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 #2,927,857 on Chainz β†—
Circulating Supply:57,975,979 XPMΒ·at block #6,841,449 Β· updates every 60s
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