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Home/Chain Registry/Block #2,792,905

Block #2,792,905

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/14/2018, 12:26:49 AM Β· Difficulty 11.6785 Β· 4,051,508 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ecdf96a8aa74363a95eff14c025fd7094d5dabacce1c4ad02797282e89773292
View on Chainz β†—

Difficulty

11.678523

Transactions

2

Size

869 B

Version

2

Bits

0badb3b2

Nonce

810,755,600

Timestamp

8/14/2018, 12:26:49 AM

Confirmations

4,051,508

Merkle Root

079d6c76535609a0e18cccbc2f096ff6c0ab2e023fc9fd0b966e1e6366f535bd
Transactions (2)
Coinbasee203da518dab23…25658dbff7937c
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
8e66ff273fc691…616eab92e0dee3
4 in β†’ 2 out160.6790 XPM669 B
AMacMFhM…iFNVuut4AQyM6rer…3jHKuYaq
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.

2.856 Γ— 10⁹⁡(96-digit number)
28565523502315034904…65732144551816854720
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
2.856 Γ— 10⁹⁡(96-digit number)
28565523502315034904…65732144551816854721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.713 Γ— 10⁹⁡(96-digit number)
57131047004630069808…31464289103633709441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.142 Γ— 10⁹⁢(97-digit number)
11426209400926013961…62928578207267418881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.285 Γ— 10⁹⁢(97-digit number)
22852418801852027923…25857156414534837761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.570 Γ— 10⁹⁢(97-digit number)
45704837603704055846…51714312829069675521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.140 Γ— 10⁹⁢(97-digit number)
91409675207408111693…03428625658139351041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.828 Γ— 10⁹⁷(98-digit number)
18281935041481622338…06857251316278702081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.656 Γ— 10⁹⁷(98-digit number)
36563870082963244677…13714502632557404161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.312 Γ— 10⁹⁷(98-digit number)
73127740165926489354…27429005265114808321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.462 Γ— 10⁹⁸(99-digit number)
14625548033185297870…54858010530229616641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.925 Γ— 10⁹⁸(99-digit number)
29251096066370595741…09716021060459233281
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 2792905

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 ecdf96a8aa74363a95eff14c025fd7094d5dabacce1c4ad02797282e89773292

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 #2,792,905 on Chainz β†—
Circulating Supply:57,999,698 XPMΒ·at block #6,844,412 Β· updates every 60s
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