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Home/Chain Registry/Block #1,091,688

Block #1,091,688

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2015, 2:47:01 AM Β· Difficulty 10.7376 Β· 5,708,372 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd3e3f9d87d825d9ae8035b5e44e3a0a2d47ce5645247cbb76b474ba85bf761f
View on Chainz β†—

Difficulty

10.737605

Transactions

1

Size

199 B

Version

2

Bits

0abcd3b3

Nonce

1,585,091,155

Timestamp

6/6/2015, 2:47:01 AM

Confirmations

5,708,372

Merkle Root

a1ffbeba28f92e774665477a519d9371af6e29d3fe047df2b163ae2e0169a227
Transactions (1)
Coinbasea1ffbeba28f92e…63ae2e0169a227
1 in β†’ 1 out8.6600 XPM109 B
AU9bn8bu…hHjzwSs5
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.

5.263 Γ— 10⁹⁴(95-digit number)
52636498592088014199…65460207587006873600
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
5.263 Γ— 10⁹⁴(95-digit number)
52636498592088014199…65460207587006873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.052 Γ— 10⁹⁡(96-digit number)
10527299718417602839…30920415174013747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.105 Γ— 10⁹⁡(96-digit number)
21054599436835205679…61840830348027494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.210 Γ— 10⁹⁡(96-digit number)
42109198873670411359…23681660696054988801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.421 Γ— 10⁹⁡(96-digit number)
84218397747340822718…47363321392109977601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.684 Γ— 10⁹⁢(97-digit number)
16843679549468164543…94726642784219955201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.368 Γ— 10⁹⁢(97-digit number)
33687359098936329087…89453285568439910401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.737 Γ— 10⁹⁢(97-digit number)
67374718197872658174…78906571136879820801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.347 Γ— 10⁹⁷(98-digit number)
13474943639574531634…57813142273759641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.694 Γ— 10⁹⁷(98-digit number)
26949887279149063269…15626284547519283201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1091688

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 dd3e3f9d87d825d9ae8035b5e44e3a0a2d47ce5645247cbb76b474ba85bf761f

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 #1,091,688 on Chainz β†—
Circulating Supply:57,644,542 XPMΒ·at block #6,800,059 Β· updates every 60s
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