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Block #250,401

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/8/2013, 11:48:48 AM Β· Difficulty 9.9683 Β· 6,545,587 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7354254e1834a22e3c4f00120fc68b5ddb41845643eb3bdd8ea665ed201fba0f
View on Chainz β†—

Height

#250,401

Difficulty

9.968259

Transactions

1

Size

188 B

Version

2

Bits

09f7dfce

Nonce

60,726

Timestamp

11/8/2013, 11:48:48 AM

Confirmations

6,545,587

Merkle Root

97698ed54507abc5843ede928b613ab4783c02e5d4c92ec072dc2cbe419b7450
Transactions (1)
Coinbase97698ed54507ab…dc2cbe419b7450
1 in β†’ 1 out10.0500 XPM97 B
ALFhmsQi…V5bffJmU
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.

1.093 Γ— 10⁹⁢(97-digit number)
10935683540405593115…05500111331910912000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.093 Γ— 10⁹⁢(97-digit number)
10935683540405593115…05500111331910911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁢(97-digit number)
21871367080811186230…11000222663821823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.374 Γ— 10⁹⁢(97-digit number)
43742734161622372461…22000445327643647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.748 Γ— 10⁹⁢(97-digit number)
87485468323244744922…44000890655287295999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.749 Γ— 10⁹⁷(98-digit number)
17497093664648948984…88001781310574591999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.499 Γ— 10⁹⁷(98-digit number)
34994187329297897969…76003562621149183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.998 Γ— 10⁹⁷(98-digit number)
69988374658595795938…52007125242298367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.399 Γ— 10⁹⁸(99-digit number)
13997674931719159187…04014250484596735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.799 Γ— 10⁹⁸(99-digit number)
27995349863438318375…08028500969193471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.599 Γ— 10⁹⁸(99-digit number)
55990699726876636750…16057001938386943999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 250401

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 7354254e1834a22e3c4f00120fc68b5ddb41845643eb3bdd8ea665ed201fba0f

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 #250,401 on Chainz β†—
Circulating Supply:57,611,999 XPMΒ·at block #6,795,987 Β· updates every 60s
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