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Home/Chain Registry/Block #1,091,577

Block #1,091,577

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2015, 1:14:59 AM Β· Difficulty 10.7365 Β· 5,734,471 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d48617953374efbf08592cb9b23b37bd5ebc6e63f7c793c35482e73f226465d
View on Chainz β†—

Difficulty

10.736532

Transactions

1

Size

199 B

Version

2

Bits

0abc8d60

Nonce

963,791,738

Timestamp

6/6/2015, 1:14:59 AM

Confirmations

5,734,471

Merkle Root

d4c1dc47b96d3295f09a8d255f336cee7ac96144dc4ba93b1558e3ac77bc52c6
Transactions (1)
Coinbased4c1dc47b96d32…58e3ac77bc52c6
1 in β†’ 1 out8.6600 XPM109 B
AVY6rA8a…8ziARTcL
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.

8.152 Γ— 10⁹⁡(96-digit number)
81523108871731076361…99670920670709621760
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
8.152 Γ— 10⁹⁡(96-digit number)
81523108871731076361…99670920670709621761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.630 Γ— 10⁹⁢(97-digit number)
16304621774346215272…99341841341419243521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.260 Γ— 10⁹⁢(97-digit number)
32609243548692430544…98683682682838487041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.521 Γ— 10⁹⁢(97-digit number)
65218487097384861089…97367365365676974081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.304 Γ— 10⁹⁷(98-digit number)
13043697419476972217…94734730731353948161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.608 Γ— 10⁹⁷(98-digit number)
26087394838953944435…89469461462707896321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.217 Γ— 10⁹⁷(98-digit number)
52174789677907888871…78938922925415792641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.043 Γ— 10⁹⁸(99-digit number)
10434957935581577774…57877845850831585281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.086 Γ— 10⁹⁸(99-digit number)
20869915871163155548…15755691701663170561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.173 Γ— 10⁹⁸(99-digit number)
41739831742326311097…31511383403326341121
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 1091577

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 0d48617953374efbf08592cb9b23b37bd5ebc6e63f7c793c35482e73f226465d

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 #1,091,577 on Chainz β†—
Circulating Supply:57,852,510 XPMΒ·at block #6,826,047 Β· updates every 60s
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