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Home/Chain Registry/Block #2,130,577

Block #2,130,577

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2017, 12:41:37 PM Β· Difficulty 10.9097 Β· 4,711,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3fabac9f54268e77a82466bc6e6b298c13a9ccae4b0f8d02a33c3a6fa9890e51
View on Chainz β†—

Difficulty

10.909731

Transactions

1

Size

200 B

Version

2

Bits

0ae8e426

Nonce

404,593,360

Timestamp

5/24/2017, 12:41:37 PM

Confirmations

4,711,259

Merkle Root

ec5eb0765ff363bd06041b2d1eb9193a2ba8438c25d471fb1c6b8e6a407952fa
Transactions (1)
Coinbaseec5eb0765ff363…6b8e6a407952fa
1 in β†’ 1 out8.3900 XPM110 B
Aavnq6vt…ay7aKt2v
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.

7.050 Γ— 10⁹⁴(95-digit number)
70505990605286071600…80190091188974616320
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
7.050 Γ— 10⁹⁴(95-digit number)
70505990605286071600…80190091188974616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.410 Γ— 10⁹⁡(96-digit number)
14101198121057214320…60380182377949232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.820 Γ— 10⁹⁡(96-digit number)
28202396242114428640…20760364755898465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.640 Γ— 10⁹⁡(96-digit number)
56404792484228857280…41520729511796930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.128 Γ— 10⁹⁢(97-digit number)
11280958496845771456…83041459023593861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.256 Γ— 10⁹⁢(97-digit number)
22561916993691542912…66082918047187722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.512 Γ— 10⁹⁢(97-digit number)
45123833987383085824…32165836094375444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.024 Γ— 10⁹⁢(97-digit number)
90247667974766171648…64331672188750888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.804 Γ— 10⁹⁷(98-digit number)
18049533594953234329…28663344377501777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.609 Γ— 10⁹⁷(98-digit number)
36099067189906468659…57326688755003555841
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 2130577

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 3fabac9f54268e77a82466bc6e6b298c13a9ccae4b0f8d02a33c3a6fa9890e51

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 #2,130,577 on Chainz β†—
Circulating Supply:57,979,061 XPMΒ·at block #6,841,835 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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