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Home/Chain Registry/Block #2,716,272

Block #2,716,272

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/22/2018, 9:52:39 AM Β· Difficulty 11.6143 Β· 4,129,070 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d504c53a600a2d06fcd3018bd757900be730b671f523f7861fda45177ac025e8
View on Chainz β†—

Difficulty

11.614345

Transactions

2

Size

572 B

Version

2

Bits

0b9d45be

Nonce

598,525,778

Timestamp

6/22/2018, 9:52:39 AM

Confirmations

4,129,070

Merkle Root

6e0b96abe313375d524b0be60754476d0131dd17868335d29caa8c03956cc2c5
Transactions (2)
Coinbasebdb4594e1c9788…2e18da29fab7aa
1 in β†’ 1 out7.4100 XPM110 B
AR9t7ma5…UrGj5Rtj
143266b67115d4…47f4252f595990
2 in β†’ 2 out9.4441 XPM372 B
AbiZw7N1…HPacQJfkAWkpQKMa…XtMNZCX7
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.

7.012 Γ— 10⁹³(94-digit number)
70120535816655730738…37065864209059062900
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
7.012 Γ— 10⁹³(94-digit number)
70120535816655730738…37065864209059062901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.402 Γ— 10⁹⁴(95-digit number)
14024107163331146147…74131728418118125801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.804 Γ— 10⁹⁴(95-digit number)
28048214326662292295…48263456836236251601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.609 Γ— 10⁹⁴(95-digit number)
56096428653324584590…96526913672472503201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.121 Γ— 10⁹⁡(96-digit number)
11219285730664916918…93053827344945006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.243 Γ— 10⁹⁡(96-digit number)
22438571461329833836…86107654689890012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.487 Γ— 10⁹⁡(96-digit number)
44877142922659667672…72215309379780025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.975 Γ— 10⁹⁡(96-digit number)
89754285845319335344…44430618759560051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.795 Γ— 10⁹⁢(97-digit number)
17950857169063867068…88861237519120102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.590 Γ— 10⁹⁢(97-digit number)
35901714338127734137…77722475038240204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.180 Γ— 10⁹⁢(97-digit number)
71803428676255468275…55444950076480409601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2716272

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 d504c53a600a2d06fcd3018bd757900be730b671f523f7861fda45177ac025e8

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 #2,716,272 on Chainz β†—
Circulating Supply:58,007,177 XPMΒ·at block #6,845,341 Β· updates every 60s
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