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Home/Chain Registry/Block #2,795,700

Block #2,795,700

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/15/2018, 10:29:43 PM Β· Difficulty 11.6806 Β· 4,049,088 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
10b4ae1e984025f3b02b767c0e12b9f21ee46f5c004fb94800dbbcddd8abe1c7
View on Chainz β†—

Difficulty

11.680567

Transactions

1

Size

201 B

Version

2

Bits

0bae39a1

Nonce

228,510,705

Timestamp

8/15/2018, 10:29:43 PM

Confirmations

4,049,088

Merkle Root

cca8d245e8844792ad08e51a6f758d44c84f65f33dcf1acdaeebbaeeb24068c6
Transactions (1)
Coinbasecca8d245e88447…ebbaeeb24068c6
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.550 Γ— 10⁹⁢(97-digit number)
15509146005418631871…93674571561441075200
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
1.550 Γ— 10⁹⁢(97-digit number)
15509146005418631871…93674571561441075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.101 Γ— 10⁹⁢(97-digit number)
31018292010837263743…87349143122882150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.203 Γ— 10⁹⁢(97-digit number)
62036584021674527487…74698286245764300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.240 Γ— 10⁹⁷(98-digit number)
12407316804334905497…49396572491528601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.481 Γ— 10⁹⁷(98-digit number)
24814633608669810995…98793144983057203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.962 Γ— 10⁹⁷(98-digit number)
49629267217339621990…97586289966114406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.925 Γ— 10⁹⁷(98-digit number)
99258534434679243980…95172579932228812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.985 Γ— 10⁹⁸(99-digit number)
19851706886935848796…90345159864457625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.970 Γ— 10⁹⁸(99-digit number)
39703413773871697592…80690319728915251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.940 Γ— 10⁹⁸(99-digit number)
79406827547743395184…61380639457830502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.588 Γ— 10⁹⁹(100-digit number)
15881365509548679036…22761278915661004801
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 2795700

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 10b4ae1e984025f3b02b767c0e12b9f21ee46f5c004fb94800dbbcddd8abe1c7

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 #2,795,700 on Chainz β†—
Circulating Supply:58,002,716 XPMΒ·at block #6,844,787 Β· updates every 60s
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