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Home/Chain Registry/Block #2,132,169

Block #2,132,169

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 2:59:06 PM Β· Difficulty 10.9100 Β· 4,712,244 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b8614d4436588f017268957173dcb656bc806da1682225ac58f23e4dc5cffa69
View on Chainz β†—

Difficulty

10.910048

Transactions

1

Size

200 B

Version

2

Bits

0ae8f8eb

Nonce

825,657,887

Timestamp

5/25/2017, 2:59:06 PM

Confirmations

4,712,244

Merkle Root

7dace9433623028aa20cfbd6d7c84d2f681226159a0d7f99f4f0fb2d439c22e4
Transactions (1)
Coinbase7dace943362302…f0fb2d439c22e4
1 in β†’ 1 out8.3900 XPM110 B
ARH8arLA…wjsRuRgZ
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.

1.517 Γ— 10⁹⁴(95-digit number)
15179942956957441656…52192192586182946480
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
1.517 Γ— 10⁹⁴(95-digit number)
15179942956957441656…52192192586182946481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.035 Γ— 10⁹⁴(95-digit number)
30359885913914883312…04384385172365892961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.071 Γ— 10⁹⁴(95-digit number)
60719771827829766624…08768770344731785921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.214 Γ— 10⁹⁡(96-digit number)
12143954365565953324…17537540689463571841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.428 Γ— 10⁹⁡(96-digit number)
24287908731131906649…35075081378927143681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.857 Γ— 10⁹⁡(96-digit number)
48575817462263813299…70150162757854287361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.715 Γ— 10⁹⁡(96-digit number)
97151634924527626599…40300325515708574721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.943 Γ— 10⁹⁢(97-digit number)
19430326984905525319…80600651031417149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.886 Γ— 10⁹⁢(97-digit number)
38860653969811050639…61201302062834298881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.772 Γ— 10⁹⁢(97-digit number)
77721307939622101279…22402604125668597761
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 2132169

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 b8614d4436588f017268957173dcb656bc806da1682225ac58f23e4dc5cffa69

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 #2,132,169 on Chainz β†—
Circulating Supply:57,999,698 XPMΒ·at block #6,844,412 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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