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Home/Chain Registry/Block #249,831

Block #249,831

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 4:27:52 AM Β· Difficulty 9.9674 Β· 6,588,700 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a39ab3bb46ab196aa15aeacaf88bcc51629deb5a47ac9248d813e6173829d83d
View on Chainz β†—

Height

#249,831

Difficulty

9.967423

Transactions

1

Size

199 B

Version

2

Bits

09f7a90b

Nonce

152,193

Timestamp

11/8/2013, 4:27:52 AM

Confirmations

6,588,700

Merkle Root

f81fe2066fc519e82f179c0bf8a5a14785b6394e476467e302b3ed9e7be1be09
Transactions (1)
Coinbasef81fe2066fc519…b3ed9e7be1be09
1 in β†’ 1 out10.0500 XPM109 B
AMasZ6ZK…DbyKh4fz
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.

8.093 Γ— 10⁹⁴(95-digit number)
80936545453563428018…72810720634015580160
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
8.093 Γ— 10⁹⁴(95-digit number)
80936545453563428018…72810720634015580161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.618 Γ— 10⁹⁡(96-digit number)
16187309090712685603…45621441268031160321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.237 Γ— 10⁹⁡(96-digit number)
32374618181425371207…91242882536062320641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.474 Γ— 10⁹⁡(96-digit number)
64749236362850742414…82485765072124641281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.294 Γ— 10⁹⁢(97-digit number)
12949847272570148482…64971530144249282561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.589 Γ— 10⁹⁢(97-digit number)
25899694545140296965…29943060288498565121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.179 Γ— 10⁹⁢(97-digit number)
51799389090280593931…59886120576997130241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.035 Γ— 10⁹⁷(98-digit number)
10359877818056118786…19772241153994260481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.071 Γ— 10⁹⁷(98-digit number)
20719755636112237572…39544482307988520961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.143 Γ— 10⁹⁷(98-digit number)
41439511272224475145…79088964615977041921
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 249831

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 a39ab3bb46ab196aa15aeacaf88bcc51629deb5a47ac9248d813e6173829d83d

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 #249,831 on Chainz β†—
Circulating Supply:57,952,527 XPMΒ·at block #6,838,530 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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