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Block #250,031

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 7:21:00 AM Β· Difficulty 9.9676 Β· 6,593,996 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8251db1537fce0b53d7bb60d1b99a16ef125b58cc6590ecf3b384153e1e5eeb5
View on Chainz β†—

Height

#250,031

Difficulty

9.967596

Transactions

1

Size

207 B

Version

2

Bits

09f7b45b

Nonce

91,587

Timestamp

11/8/2013, 7:21:00 AM

Confirmations

6,593,996

Merkle Root

ce6a7202a84801fabb6b0297824a95be08a4f59919057c47672686088fc8f9ac
Transactions (1)
Coinbasece6a7202a84801…2686088fc8f9ac
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.978 Γ— 10⁹⁢(97-digit number)
19782802491884783485…03203693201857495040
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
1.978 Γ— 10⁹⁢(97-digit number)
19782802491884783485…03203693201857495041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.956 Γ— 10⁹⁢(97-digit number)
39565604983769566970…06407386403714990081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.913 Γ— 10⁹⁢(97-digit number)
79131209967539133941…12814772807429980161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.582 Γ— 10⁹⁷(98-digit number)
15826241993507826788…25629545614859960321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.165 Γ— 10⁹⁷(98-digit number)
31652483987015653576…51259091229719920641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.330 Γ— 10⁹⁷(98-digit number)
63304967974031307153…02518182459439841281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.266 Γ— 10⁹⁸(99-digit number)
12660993594806261430…05036364918879682561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.532 Γ— 10⁹⁸(99-digit number)
25321987189612522861…10072729837759365121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.064 Γ— 10⁹⁸(99-digit number)
50643974379225045722…20145459675518730241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.012 Γ— 10⁹⁹(100-digit number)
10128794875845009144…40290919351037460481
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 250031

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 8251db1537fce0b53d7bb60d1b99a16ef125b58cc6590ecf3b384153e1e5eeb5

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 #250,031 on Chainz β†—
Circulating Supply:57,996,592 XPMΒ·at block #6,844,026 Β· updates every 60s
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