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Block #342,735

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/4/2014, 6:27:58 AM Β· Difficulty 10.1615 Β· 6,468,973 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7f4eed389f33768a8ccb1ee16349033cb85a9143f2cfae53456f872eb5cb2b3f
View on Chainz β†—

Height

#342,735

Difficulty

10.161527

Transactions

2

Size

427 B

Version

2

Bits

0a2959db

Nonce

173,967

Timestamp

1/4/2014, 6:27:58 AM

Confirmations

6,468,973

Merkle Root

15e70b19a642063be5614a24cacff4ab2d32d0ec851a400bea2409974af8afcf
Transactions (2)
Coinbase3c442c3e10b64f…427176cc89669a
1 in β†’ 1 out9.6800 XPM109 B
AcFvuCxj…kgbx2M93
80879afca7b26a…071a4e8090ed38
1 in β†’ 2 out3.5624 XPM227 B
AHPk7e2X…h1o6etmVAddQ8Nb5…XsNKaPQ1
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.

2.640 Γ— 10⁹⁢(97-digit number)
26401578881126869385…46365857001683760000
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
2.640 Γ— 10⁹⁢(97-digit number)
26401578881126869385…46365857001683760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.280 Γ— 10⁹⁢(97-digit number)
52803157762253738771…92731714003367520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.056 Γ— 10⁹⁷(98-digit number)
10560631552450747754…85463428006735040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.112 Γ— 10⁹⁷(98-digit number)
21121263104901495508…70926856013470080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.224 Γ— 10⁹⁷(98-digit number)
42242526209802991017…41853712026940160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.448 Γ— 10⁹⁷(98-digit number)
84485052419605982034…83707424053880320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.689 Γ— 10⁹⁸(99-digit number)
16897010483921196406…67414848107760640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.379 Γ— 10⁹⁸(99-digit number)
33794020967842392813…34829696215521280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.758 Γ— 10⁹⁸(99-digit number)
67588041935684785627…69659392431042560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.351 Γ— 10⁹⁹(100-digit number)
13517608387136957125…39318784862085120001
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 342735

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 7f4eed389f33768a8ccb1ee16349033cb85a9143f2cfae53456f872eb5cb2b3f

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 #342,735 on Chainz β†—
Circulating Supply:57,737,775 XPMΒ·at block #6,811,707 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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