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Home/Chain Registry/Block #2,297,108

Block #2,297,108

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2017, 12:33:57 PM Β· Difficulty 10.9484 Β· 4,541,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
da6e33f9b1c2904a5010f388445232a2c9e823ff76d15ec10ced9fc23b31a665
View on Chainz β†—

Difficulty

10.948364

Transactions

2

Size

574 B

Version

2

Bits

0af2c7ff

Nonce

985,885,657

Timestamp

9/15/2017, 12:33:57 PM

Confirmations

4,541,451

Merkle Root

155a1ac09185848885dde188ef8e48b008ed294f9a3c77cf046cb26368a45acd
Transactions (2)
Coinbaseaf5f4ef4ff7aa5…b6e91f62a27cfc
1 in β†’ 1 out8.3400 XPM110 B
AJwgt4LD…qBLkKKv6
66c98aa1541cc0…6d764549ec343a
2 in β†’ 2 out81998.7154 XPM375 B
AK2bipW8…cgbaenXuAQPpMFWK…33tW4HFQ
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.

2.062 Γ— 10⁹³(94-digit number)
20624471367547845736…79221172720971507040
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
2.062 Γ— 10⁹³(94-digit number)
20624471367547845736…79221172720971507041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.124 Γ— 10⁹³(94-digit number)
41248942735095691472…58442345441943014081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.249 Γ— 10⁹³(94-digit number)
82497885470191382944…16884690883886028161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.649 Γ— 10⁹⁴(95-digit number)
16499577094038276588…33769381767772056321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.299 Γ— 10⁹⁴(95-digit number)
32999154188076553177…67538763535544112641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.599 Γ— 10⁹⁴(95-digit number)
65998308376153106355…35077527071088225281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.319 Γ— 10⁹⁡(96-digit number)
13199661675230621271…70155054142176450561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.639 Γ— 10⁹⁡(96-digit number)
26399323350461242542…40310108284352901121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.279 Γ— 10⁹⁡(96-digit number)
52798646700922485084…80620216568705802241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.055 Γ— 10⁹⁢(97-digit number)
10559729340184497016…61240433137411604481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.111 Γ— 10⁹⁢(97-digit number)
21119458680368994033…22480866274823208961
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 2297108

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 da6e33f9b1c2904a5010f388445232a2c9e823ff76d15ec10ced9fc23b31a665

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 #2,297,108 on Chainz β†—
Circulating Supply:57,952,756 XPMΒ·at block #6,838,558 Β· updates every 60s
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