XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #276,787

Block #276,787

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 8:00:52 AM Β· Difficulty 9.9642 Β· 6,524,061 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aab2cb8192dc8caa79643ee4335f73a6f5220dde6b1cf6daab82957e3a703fb2
View on Chainz β†—

Height

#276,787

Difficulty

9.964205

Transactions

1

Size

206 B

Version

2

Bits

09f6d623

Nonce

476,801

Timestamp

11/27/2013, 8:00:52 AM

Confirmations

6,524,061

Merkle Root

f9d7f84d298c01274305bed07f77386e69d5577ce11b968b01756e59efabc983
Transactions (1)
Coinbasef9d7f84d298c01…756e59efabc983
1 in β†’ 1 out10.0600 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.

5.557 Γ— 10⁹⁡(96-digit number)
55576596052904346992…17468370419084942920
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
5.557 Γ— 10⁹⁡(96-digit number)
55576596052904346992…17468370419084942921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.111 Γ— 10⁹⁢(97-digit number)
11115319210580869398…34936740838169885841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.223 Γ— 10⁹⁢(97-digit number)
22230638421161738797…69873481676339771681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.446 Γ— 10⁹⁢(97-digit number)
44461276842323477594…39746963352679543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.892 Γ— 10⁹⁢(97-digit number)
88922553684646955188…79493926705359086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.778 Γ— 10⁹⁷(98-digit number)
17784510736929391037…58987853410718173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.556 Γ— 10⁹⁷(98-digit number)
35569021473858782075…17975706821436346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.113 Γ— 10⁹⁷(98-digit number)
71138042947717564150…35951413642872693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.422 Γ— 10⁹⁸(99-digit number)
14227608589543512830…71902827285745387521
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 276787

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 aab2cb8192dc8caa79643ee4335f73a6f5220dde6b1cf6daab82957e3a703fb2

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 #276,787 on Chainz β†—
Circulating Supply:57,650,844 XPMΒ·at block #6,800,847 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK