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Home/Chain Registry/Block #839,339

Block #839,339

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/4/2014, 8:13:34 AM Β· Difficulty 10.9746 Β· 6,003,779 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0f627ba939e2d562c1f69efd0008355e008efe2bcd01bfb0298b09729946b4ae
View on Chainz β†—

Height

#839,339

Difficulty

10.974646

Transactions

2

Size

432 B

Version

2

Bits

0af9826c

Nonce

731,565,081

Timestamp

12/4/2014, 8:13:34 AM

Confirmations

6,003,779

Merkle Root

b4f4e96e16fadbec6506bb9668c8105d5f994d54309249a03164c4b9a2631c5e
Transactions (2)
Coinbasecbaffa56335724…6c284d81e667cf
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
4b4dccb12a7734…8fa16ac65c4b0c
1 in β†’ 2 out5.2375 XPM225 B
AW6xKVVP…sFp5odmTANts68oj…zLVXKCqZ
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.

1.796 Γ— 10⁹⁸(99-digit number)
17965851316409934831…22172019665800125440
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
1.796 Γ— 10⁹⁸(99-digit number)
17965851316409934831…22172019665800125441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.593 Γ— 10⁹⁸(99-digit number)
35931702632819869663…44344039331600250881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.186 Γ— 10⁹⁸(99-digit number)
71863405265639739327…88688078663200501761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.437 Γ— 10⁹⁹(100-digit number)
14372681053127947865…77376157326401003521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.874 Γ— 10⁹⁹(100-digit number)
28745362106255895730…54752314652802007041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.749 Γ— 10⁹⁹(100-digit number)
57490724212511791461…09504629305604014081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.149 Γ— 10¹⁰⁰(101-digit number)
11498144842502358292…19009258611208028161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.299 Γ— 10¹⁰⁰(101-digit number)
22996289685004716584…38018517222416056321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.599 Γ— 10¹⁰⁰(101-digit number)
45992579370009433169…76037034444832112641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.198 Γ— 10¹⁰⁰(101-digit number)
91985158740018866338…52074068889664225281
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 839339

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 0f627ba939e2d562c1f69efd0008355e008efe2bcd01bfb0298b09729946b4ae

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 #839,339 on Chainz β†—
Circulating Supply:57,989,310 XPMΒ·at block #6,843,117 Β· updates every 60s
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