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Block #1,090,715

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/5/2015, 11:37:02 AM Β· Difficulty 10.7342 Β· 5,734,910 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
39e88fc686b3aa4c84f2086248218fc0ab40ecd31fb62e904612ebf1ec9c4c2a
View on Chainz β†—

Difficulty

10.734228

Transactions

1

Size

243 B

Version

2

Bits

0abbf660

Nonce

197,500,614

Timestamp

6/5/2015, 11:37:02 AM

Confirmations

5,734,910

Merkle Root

3cad80fefc155640fe07d6626b9ec029fbb48495f672f779523401f1bf3ae884
Transactions (1)
Coinbase3cad80fefc1556…3401f1bf3ae884
1 in β†’ 2 out8.6700 XPM152 B
AKE3G8fG…CxqrmRMyALPu3s2c…EJXLjVFh
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.

1.737 Γ— 10⁹⁷(98-digit number)
17372374340045485706…20380611798242344960
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
1.737 Γ— 10⁹⁷(98-digit number)
17372374340045485706…20380611798242344961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.474 Γ— 10⁹⁷(98-digit number)
34744748680090971413…40761223596484689921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.948 Γ— 10⁹⁷(98-digit number)
69489497360181942827…81522447192969379841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.389 Γ— 10⁹⁸(99-digit number)
13897899472036388565…63044894385938759681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.779 Γ— 10⁹⁸(99-digit number)
27795798944072777131…26089788771877519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.559 Γ— 10⁹⁸(99-digit number)
55591597888145554262…52179577543755038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.111 Γ— 10⁹⁹(100-digit number)
11118319577629110852…04359155087510077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.223 Γ— 10⁹⁹(100-digit number)
22236639155258221704…08718310175020154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.447 Γ— 10⁹⁹(100-digit number)
44473278310516443409…17436620350040309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.894 Γ— 10⁹⁹(100-digit number)
88946556621032886819…34873240700080619521
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 1090715

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 39e88fc686b3aa4c84f2086248218fc0ab40ecd31fb62e904612ebf1ec9c4c2a

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 #1,090,715 on Chainz β†—
Circulating Supply:57,849,102 XPMΒ·at block #6,825,624 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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