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Block #310,765

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/14/2013, 5:43:13 AM Β· Difficulty 9.9953 Β· 6,484,627 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ffee21d5ecf9512e351adad03e6e01d3de32f5e59f5b5d1e8a08c104b16b117
View on Chainz β†—

Height

#310,765

Difficulty

9.995285

Transactions

1

Size

206 B

Version

2

Bits

09fecafa

Nonce

11,769

Timestamp

12/14/2013, 5:43:13 AM

Confirmations

6,484,627

Merkle Root

2bb2e41d00d6e2c167a97e08cc28a06a8701d9664d1b31db8697b5c97400203c
Transactions (1)
Coinbase2bb2e41d00d6e2…97b5c97400203c
1 in β†’ 1 out9.9900 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.

3.158 Γ— 10⁹⁴(95-digit number)
31581183462860749604…42345125200491340800
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
3.158 Γ— 10⁹⁴(95-digit number)
31581183462860749604…42345125200491340801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.316 Γ— 10⁹⁴(95-digit number)
63162366925721499208…84690250400982681601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.263 Γ— 10⁹⁡(96-digit number)
12632473385144299841…69380500801965363201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.526 Γ— 10⁹⁡(96-digit number)
25264946770288599683…38761001603930726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.052 Γ— 10⁹⁡(96-digit number)
50529893540577199366…77522003207861452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.010 Γ— 10⁹⁢(97-digit number)
10105978708115439873…55044006415722905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.021 Γ— 10⁹⁢(97-digit number)
20211957416230879746…10088012831445811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.042 Γ— 10⁹⁢(97-digit number)
40423914832461759493…20176025662891622401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.084 Γ— 10⁹⁢(97-digit number)
80847829664923518986…40352051325783244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.616 Γ— 10⁹⁷(98-digit number)
16169565932984703797…80704102651566489601
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 310765

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 1ffee21d5ecf9512e351adad03e6e01d3de32f5e59f5b5d1e8a08c104b16b117

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 #310,765 on Chainz β†—
Circulating Supply:57,607,196 XPMΒ·at block #6,795,391 Β· updates every 60s
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