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Block #163,019

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 5:11:01 PM Β· Difficulty 9.8617 Β· 6,664,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76cfe896be0cdf01e616889c91a7a9aa93c1f8a5f274b7e2915ae69a1fd973d5
View on Chainz β†—

Height

#163,019

Difficulty

9.861661

Transactions

1

Size

201 B

Version

2

Bits

09dc95d2

Nonce

231,241

Timestamp

9/13/2013, 5:11:01 PM

Confirmations

6,664,017

Merkle Root

e91ce2122ea1aaf81adc12b2fa8e7a99b3cbe0f404fc58f9abc206bc6f744632
Transactions (1)
Coinbasee91ce2122ea1aa…c206bc6f744632
1 in β†’ 1 out10.2700 XPM110 B
APcNcguo…D6ZdWA2f
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.

1.249 Γ— 10⁹⁢(97-digit number)
12490906865225286878…38107402058257712000
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
1.249 Γ— 10⁹⁢(97-digit number)
12490906865225286878…38107402058257712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.498 Γ— 10⁹⁢(97-digit number)
24981813730450573757…76214804116515424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.996 Γ— 10⁹⁢(97-digit number)
49963627460901147515…52429608233030848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.992 Γ— 10⁹⁢(97-digit number)
99927254921802295030…04859216466061696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.998 Γ— 10⁹⁷(98-digit number)
19985450984360459006…09718432932123392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.997 Γ— 10⁹⁷(98-digit number)
39970901968720918012…19436865864246784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.994 Γ— 10⁹⁷(98-digit number)
79941803937441836024…38873731728493568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.598 Γ— 10⁹⁸(99-digit number)
15988360787488367204…77747463456987136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.197 Γ— 10⁹⁸(99-digit number)
31976721574976734409…55494926913974272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.395 Γ— 10⁹⁸(99-digit number)
63953443149953468819…10989853827948544001
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 163019

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 76cfe896be0cdf01e616889c91a7a9aa93c1f8a5f274b7e2915ae69a1fd973d5

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 #163,019 on Chainz β†—
Circulating Supply:57,860,468 XPMΒ·at block #6,827,035 Β· updates every 60s
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