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Block #317,176

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2013, 12:22:17 PM Β· Difficulty 10.1542 Β· 6,478,411 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d0a01fdbb1e9b5d5bd697b2919705ae5844a99c8a0247433777dd6cb3b54e110
View on Chainz β†—

Height

#317,176

Difficulty

10.154166

Transactions

1

Size

206 B

Version

2

Bits

0a277774

Nonce

45,518

Timestamp

12/17/2013, 12:22:17 PM

Confirmations

6,478,411

Merkle Root

f8af3d8b6de7e783ce5c4e67304e99b49d8bf0154f7eac1d795a50328da55e89
Transactions (1)
Coinbasef8af3d8b6de7e7…5a50328da55e89
1 in β†’ 1 out9.6800 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.

1.071 Γ— 10⁹⁡(96-digit number)
10711645953035793517…67730528176443238400
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
1.071 Γ— 10⁹⁡(96-digit number)
10711645953035793517…67730528176443238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.142 Γ— 10⁹⁡(96-digit number)
21423291906071587034…35461056352886476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.284 Γ— 10⁹⁡(96-digit number)
42846583812143174068…70922112705772953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.569 Γ— 10⁹⁡(96-digit number)
85693167624286348137…41844225411545907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.713 Γ— 10⁹⁢(97-digit number)
17138633524857269627…83688450823091814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.427 Γ— 10⁹⁢(97-digit number)
34277267049714539254…67376901646183628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.855 Γ— 10⁹⁢(97-digit number)
68554534099429078509…34753803292367257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.371 Γ— 10⁹⁷(98-digit number)
13710906819885815701…69507606584734515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.742 Γ— 10⁹⁷(98-digit number)
27421813639771631403…39015213169469030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.484 Γ— 10⁹⁷(98-digit number)
54843627279543262807…78030426338938060801
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 317176

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 d0a01fdbb1e9b5d5bd697b2919705ae5844a99c8a0247433777dd6cb3b54e110

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 #317,176 on Chainz β†—
Circulating Supply:57,608,759 XPMΒ·at block #6,795,586 Β· updates every 60s
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