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Block #277,995

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 7:31:12 PM Β· Difficulty 9.9677 Β· 6,518,026 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
700fa6244af4fca4e0ee7fcfb5c59a908b0e702a8f632cf715746c4fde072572
View on Chainz β†—

Height

#277,995

Difficulty

9.967740

Transactions

1

Size

207 B

Version

2

Bits

09f7bdd6

Nonce

1,356

Timestamp

11/27/2013, 7:31:12 PM

Confirmations

6,518,026

Merkle Root

db13b8b298b5135d16f952d439efa055c89e3b3409aa3a058568f90ddb0b589a
Transactions (1)
Coinbasedb13b8b298b513…68f90ddb0b589a
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.894 Γ— 10⁹⁢(97-digit number)
68948764568647797772…65908720295220746400
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
6.894 Γ— 10⁹⁢(97-digit number)
68948764568647797772…65908720295220746401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.378 Γ— 10⁹⁷(98-digit number)
13789752913729559554…31817440590441492801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.757 Γ— 10⁹⁷(98-digit number)
27579505827459119108…63634881180882985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.515 Γ— 10⁹⁷(98-digit number)
55159011654918238217…27269762361765971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.103 Γ— 10⁹⁸(99-digit number)
11031802330983647643…54539524723531942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.206 Γ— 10⁹⁸(99-digit number)
22063604661967295287…09079049447063884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.412 Γ— 10⁹⁸(99-digit number)
44127209323934590574…18158098894127769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.825 Γ— 10⁹⁸(99-digit number)
88254418647869181148…36316197788255539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.765 Γ— 10⁹⁹(100-digit number)
17650883729573836229…72632395576511078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.530 Γ— 10⁹⁹(100-digit number)
35301767459147672459…45264791153022156801
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 277995

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 700fa6244af4fca4e0ee7fcfb5c59a908b0e702a8f632cf715746c4fde072572

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 #277,995 on Chainz β†—
Circulating Supply:57,612,260 XPMΒ·at block #6,796,020 Β· updates every 60s
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