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Block #331,770

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/27/2013, 2:10:18 PM Β· Difficulty 10.1724 Β· 6,469,191 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a7cb1e13804c41cfcbb32c34af19f5d2a86b05da61dcfff971c62e7a9bdebf8
View on Chainz β†—

Height

#331,770

Difficulty

10.172367

Transactions

1

Size

207 B

Version

2

Bits

0a2c203b

Nonce

51,507

Timestamp

12/27/2013, 2:10:18 PM

Confirmations

6,469,191

Merkle Root

48feda4a49784eee89503cb1470f0aa0c7988c65130930f56450239650457252
Transactions (1)
Coinbase48feda4a49784e…50239650457252
1 in β†’ 1 out9.6500 XPM116 B
AbwWkWZt…kawDhufa
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.

9.714 Γ— 10⁹⁢(97-digit number)
97144035480863856629…82028190522527973760
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
9.714 Γ— 10⁹⁢(97-digit number)
97144035480863856629…82028190522527973761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.942 Γ— 10⁹⁷(98-digit number)
19428807096172771325…64056381045055947521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.885 Γ— 10⁹⁷(98-digit number)
38857614192345542651…28112762090111895041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.771 Γ— 10⁹⁷(98-digit number)
77715228384691085303…56225524180223790081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.554 Γ— 10⁹⁸(99-digit number)
15543045676938217060…12451048360447580161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.108 Γ— 10⁹⁸(99-digit number)
31086091353876434121…24902096720895160321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.217 Γ— 10⁹⁸(99-digit number)
62172182707752868242…49804193441790320641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.243 Γ— 10⁹⁹(100-digit number)
12434436541550573648…99608386883580641281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.486 Γ— 10⁹⁹(100-digit number)
24868873083101147297…99216773767161282561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.973 Γ— 10⁹⁹(100-digit number)
49737746166202294594…98433547534322565121
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 331770

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 5a7cb1e13804c41cfcbb32c34af19f5d2a86b05da61dcfff971c62e7a9bdebf8

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 #331,770 on Chainz β†—
Circulating Supply:57,651,745 XPMΒ·at block #6,800,960 Β· updates every 60s
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