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Home/Chain Registry/Block #291,070

Block #291,070

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2013, 12:09:17 AM Β· Difficulty 9.9896 Β· 6,522,962 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a7e2c2cf97c0cd100c564b60abfac8a2cd0f62f166c30df86f48361cfb87396
View on Chainz β†—

Height

#291,070

Difficulty

9.989640

Transactions

1

Size

199 B

Version

2

Bits

09fd5912

Nonce

95,709

Timestamp

12/3/2013, 12:09:17 AM

Confirmations

6,522,962

Merkle Root

991be3728f5cbdbf7a7a249a0251909bbafc59414cbaec416bc726779be09f20
Transactions (1)
Coinbase991be3728f5cbd…c726779be09f20
1 in β†’ 1 out10.0100 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.011 Γ— 10⁹²(93-digit number)
20117076950320886741…99895379861123072000
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
2.011 Γ— 10⁹²(93-digit number)
20117076950320886741…99895379861123072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.023 Γ— 10⁹²(93-digit number)
40234153900641773482…99790759722246144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.046 Γ— 10⁹²(93-digit number)
80468307801283546964…99581519444492288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.609 Γ— 10⁹³(94-digit number)
16093661560256709392…99163038888984576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.218 Γ— 10⁹³(94-digit number)
32187323120513418785…98326077777969152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.437 Γ— 10⁹³(94-digit number)
64374646241026837571…96652155555938304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.287 Γ— 10⁹⁴(95-digit number)
12874929248205367514…93304311111876608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.574 Γ— 10⁹⁴(95-digit number)
25749858496410735028…86608622223753216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.149 Γ— 10⁹⁴(95-digit number)
51499716992821470057…73217244447506432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.029 Γ— 10⁹⁡(96-digit number)
10299943398564294011…46434488895012864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.059 Γ— 10⁹⁡(96-digit number)
20599886797128588022…92868977790025728001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 291070

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 5a7e2c2cf97c0cd100c564b60abfac8a2cd0f62f166c30df86f48361cfb87396

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 #291,070 on Chainz β†—
Circulating Supply:57,756,331 XPMΒ·at block #6,814,031 Β· updates every 60s
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