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Block #320,761

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/19/2013, 9:05:26 PM Β· Difficulty 10.1854 Β· 6,474,924 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2b42d418451c2c195ef5a06fd18ea35e321d58e1d54c0097cebbe4c38251e7f
View on Chainz β†—

Height

#320,761

Difficulty

10.185443

Transactions

1

Size

205 B

Version

2

Bits

0a2f7939

Nonce

302,133

Timestamp

12/19/2013, 9:05:26 PM

Confirmations

6,474,924

Merkle Root

15d11a7ea29bd26c574efe4895b826245fcee4a14656d84432218766c1e498fc
Transactions (1)
Coinbase15d11a7ea29bd2…218766c1e498fc
1 in β†’ 1 out9.6200 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.

1.089 Γ— 10⁹¹(92-digit number)
10890852515793750746…70897259690992525920
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
1.089 Γ— 10⁹¹(92-digit number)
10890852515793750746…70897259690992525921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.178 Γ— 10⁹¹(92-digit number)
21781705031587501492…41794519381985051841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.356 Γ— 10⁹¹(92-digit number)
43563410063175002985…83589038763970103681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.712 Γ— 10⁹¹(92-digit number)
87126820126350005970…67178077527940207361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.742 Γ— 10⁹²(93-digit number)
17425364025270001194…34356155055880414721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.485 Γ— 10⁹²(93-digit number)
34850728050540002388…68712310111760829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.970 Γ— 10⁹²(93-digit number)
69701456101080004776…37424620223521658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.394 Γ— 10⁹³(94-digit number)
13940291220216000955…74849240447043317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.788 Γ— 10⁹³(94-digit number)
27880582440432001910…49698480894086635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.576 Γ— 10⁹³(94-digit number)
55761164880864003820…99396961788173271041
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 320761

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 d2b42d418451c2c195ef5a06fd18ea35e321d58e1d54c0097cebbe4c38251e7f

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 #320,761 on Chainz β†—
Circulating Supply:57,609,549 XPMΒ·at block #6,795,684 Β· updates every 60s
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