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Block #249,600

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/8/2013, 1:27:29 AM Β· Difficulty 9.9671 Β· 6,574,955 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b40ed85bb73dc2b5b04259e9c94024f0658dd7510ecdf637bfc4b86e6baf7f70
View on Chainz β†—

Height

#249,600

Difficulty

9.967089

Transactions

1

Size

231 B

Version

2

Bits

09f79329

Nonce

36,694

Timestamp

11/8/2013, 1:27:29 AM

Confirmations

6,574,955

Merkle Root

699ee806acb74b24f48fb7a71e20887023298e3aa89b8fd43ab49606d22803aa
Transactions (1)
Coinbase699ee806acb74b…b49606d22803aa
1 in β†’ 2 out10.0500 XPM141 B
AKcbk49N…GJbKa7j1ALfEGCwh…VawujfMm
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.

1.688 Γ— 10⁹⁴(95-digit number)
16883637137085036596…43124188324719841050
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
1.688 Γ— 10⁹⁴(95-digit number)
16883637137085036596…43124188324719841049
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.376 Γ— 10⁹⁴(95-digit number)
33767274274170073193…86248376649439682099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.753 Γ— 10⁹⁴(95-digit number)
67534548548340146386…72496753298879364199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.350 Γ— 10⁹⁡(96-digit number)
13506909709668029277…44993506597758728399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.701 Γ— 10⁹⁡(96-digit number)
27013819419336058554…89987013195517456799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.402 Γ— 10⁹⁡(96-digit number)
54027638838672117108…79974026391034913599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁢(97-digit number)
10805527767734423421…59948052782069827199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.161 Γ— 10⁹⁢(97-digit number)
21611055535468846843…19896105564139654399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.322 Γ— 10⁹⁢(97-digit number)
43222111070937693687…39792211128279308799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.644 Γ— 10⁹⁢(97-digit number)
86444222141875387374…79584422256558617599
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 249600

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 b40ed85bb73dc2b5b04259e9c94024f0658dd7510ecdf637bfc4b86e6baf7f70

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 #249,600 on Chainz β†—
Circulating Supply:57,840,503 XPMΒ·at block #6,824,554 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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