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Block #163,556

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2013, 1:59:20 AM Β· Difficulty 9.8619 Β· 6,631,131 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f70b541e159fe472600ea4b6908e13180b2ec3d067893c16b3ce8a0a4daea7a6
View on Chainz β†—

Height

#163,556

Difficulty

9.861916

Transactions

2

Size

503 B

Version

2

Bits

09dca68d

Nonce

33,568

Timestamp

9/14/2013, 1:59:20 AM

Confirmations

6,631,131

Merkle Root

b5a5158bc325baa805848ac578ec96c5a47c847979815f90cbd589bdda90cb58
Transactions (2)
Coinbasef5132babeb3e75…093344c094a842
1 in β†’ 1 out10.2800 XPM109 B
AVR6qYPZ…9Mf7ugde
857ad31dd345fe…66198ccec7b80d
2 in β†’ 2 out20.5100 XPM306 B
ATXtZ6gN…62iJEfZJARVq2yYk…Hi8Q4Wuu
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.

4.421 Γ— 10⁸⁹(90-digit number)
44213494516700093099…87632546775085091840
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
4.421 Γ— 10⁸⁹(90-digit number)
44213494516700093099…87632546775085091841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.842 Γ— 10⁸⁹(90-digit number)
88426989033400186199…75265093550170183681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.768 Γ— 10⁹⁰(91-digit number)
17685397806680037239…50530187100340367361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.537 Γ— 10⁹⁰(91-digit number)
35370795613360074479…01060374200680734721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.074 Γ— 10⁹⁰(91-digit number)
70741591226720148959…02120748401361469441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.414 Γ— 10⁹¹(92-digit number)
14148318245344029791…04241496802722938881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.829 Γ— 10⁹¹(92-digit number)
28296636490688059583…08482993605445877761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.659 Γ— 10⁹¹(92-digit number)
56593272981376119167…16965987210891755521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.131 Γ— 10⁹²(93-digit number)
11318654596275223833…33931974421783511041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.263 Γ— 10⁹²(93-digit number)
22637309192550447667…67863948843567022081
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 163556

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 f70b541e159fe472600ea4b6908e13180b2ec3d067893c16b3ce8a0a4daea7a6

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 #163,556 on Chainz β†—
Circulating Supply:57,601,549 XPMΒ·at block #6,794,686 Β· updates every 60s
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