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Block #277,849

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 5:57:48 PM Β· Difficulty 9.9674 Β· 6,546,903 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5368f0b6f9e8a06064e9380dca3eadfbbddfe33974b18a538ef44ec1d03bc6e9
View on Chainz β†—

Height

#277,849

Difficulty

9.967399

Transactions

1

Size

201 B

Version

2

Bits

09f7a77b

Nonce

5,906

Timestamp

11/27/2013, 5:57:48 PM

Confirmations

6,546,903

Merkle Root

a0474128f0ca395d08d0ba5bc68ec871227dab98e7f7685dda365ddfdea3314e
Transactions (1)
Coinbasea0474128f0ca39…365ddfdea3314e
1 in β†’ 1 out10.0500 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.

1.995 Γ— 10⁹⁢(97-digit number)
19954444804846247292…22328758548331776000
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
1.995 Γ— 10⁹⁢(97-digit number)
19954444804846247292…22328758548331776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.990 Γ— 10⁹⁢(97-digit number)
39908889609692494584…44657517096663552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.981 Γ— 10⁹⁢(97-digit number)
79817779219384989169…89315034193327104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.596 Γ— 10⁹⁷(98-digit number)
15963555843876997833…78630068386654208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.192 Γ— 10⁹⁷(98-digit number)
31927111687753995667…57260136773308416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.385 Γ— 10⁹⁷(98-digit number)
63854223375507991335…14520273546616832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.277 Γ— 10⁹⁸(99-digit number)
12770844675101598267…29040547093233664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.554 Γ— 10⁹⁸(99-digit number)
25541689350203196534…58081094186467328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.108 Γ— 10⁹⁸(99-digit number)
51083378700406393068…16162188372934656001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 277849

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 5368f0b6f9e8a06064e9380dca3eadfbbddfe33974b18a538ef44ec1d03bc6e9

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 #277,849 on Chainz β†—
Circulating Supply:57,842,087 XPMΒ·at block #6,824,751 Β· updates every 60s
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