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Block #39,356

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 1:21:15 PM Β· Difficulty 8.3089 Β· 6,771,799 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1444cdb4ffafe4e9b597d08b6400b980e644636f5b9901a7bfed184c01d2538a
View on Chainz β†—

Height

#39,356

Difficulty

8.308934

Transactions

1

Size

200 B

Version

2

Bits

084f164c

Nonce

442

Timestamp

7/14/2013, 1:21:15 PM

Confirmations

6,771,799

Merkle Root

8eb4030204106c5ee69db4e70f2c95772fd8176a28b603b137b0b572e715924f
Transactions (1)
Coinbase8eb4030204106c…b0b572e715924f
1 in β†’ 1 out14.4700 XPM109 B
AKsLKPc8…zkBgUqcr
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.

1.360 Γ— 10⁹⁸(99-digit number)
13603727970447481615…62908977917857781370
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
1.360 Γ— 10⁹⁸(99-digit number)
13603727970447481615…62908977917857781371
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.720 Γ— 10⁹⁸(99-digit number)
27207455940894963231…25817955835715562741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.441 Γ— 10⁹⁸(99-digit number)
54414911881789926463…51635911671431125481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.088 Γ— 10⁹⁹(100-digit number)
10882982376357985292…03271823342862250961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.176 Γ— 10⁹⁹(100-digit number)
21765964752715970585…06543646685724501921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.353 Γ— 10⁹⁹(100-digit number)
43531929505431941170…13087293371449003841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.706 Γ— 10⁹⁹(100-digit number)
87063859010863882341…26174586742898007681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.741 Γ— 10¹⁰⁰(101-digit number)
17412771802172776468…52349173485796015361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 39356

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 1444cdb4ffafe4e9b597d08b6400b980e644636f5b9901a7bfed184c01d2538a

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 #39,356 on Chainz β†—
Circulating Supply:57,733,351 XPMΒ·at block #6,811,154 Β· updates every 60s
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