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Block #63,269

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 12:22:41 AM Β· Difficulty 8.9787 Β· 6,737,325 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
371e617947e0b5f21e814c511d6c43abcff2fcb2aea525034b1b416cfddfaac2
View on Chainz β†—

Height

#63,269

Difficulty

8.978733

Transactions

1

Size

199 B

Version

2

Bits

08fa8e3a

Nonce

737

Timestamp

7/19/2013, 12:22:41 AM

Confirmations

6,737,325

Merkle Root

20cc41c8b985959e5122d8f3c896f96da5da1e9a53644087e88c97a3fe398f43
Transactions (1)
Coinbase20cc41c8b98595…8c97a3fe398f43
1 in β†’ 1 out12.3900 XPM110 B
AdaqGs2t…veY4HvWf
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— 10⁹²(93-digit number)
15179962834337288974…60766355402485290740
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— 10⁹²(93-digit number)
15179962834337288974…60766355402485290741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.035 Γ— 10⁹²(93-digit number)
30359925668674577948…21532710804970581481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.071 Γ— 10⁹²(93-digit number)
60719851337349155897…43065421609941162961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.214 Γ— 10⁹³(94-digit number)
12143970267469831179…86130843219882325921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.428 Γ— 10⁹³(94-digit number)
24287940534939662358…72261686439764651841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.857 Γ— 10⁹³(94-digit number)
48575881069879324717…44523372879529303681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.715 Γ— 10⁹³(94-digit number)
97151762139758649435…89046745759058607361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.943 Γ— 10⁹⁴(95-digit number)
19430352427951729887…78093491518117214721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.886 Γ— 10⁹⁴(95-digit number)
38860704855903459774…56186983036234429441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 63269

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 371e617947e0b5f21e814c511d6c43abcff2fcb2aea525034b1b416cfddfaac2

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 #63,269 on Chainz β†—
Circulating Supply:57,648,811 XPMΒ·at block #6,800,593 Β· updates every 60s
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