XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #277,715

Block #277,715

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 4:35:51 PM Β· Difficulty 9.9671 Β· 6,553,279 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23a677fe4704bf9d281e45b4467fe4e940fdb750291aa8b8741b5d024b56f6cc
View on Chainz β†—

Height

#277,715

Difficulty

9.967064

Transactions

2

Size

427 B

Version

2

Bits

09f79183

Nonce

34,664

Timestamp

11/27/2013, 4:35:51 PM

Confirmations

6,553,279

Merkle Root

2b56195878a841b0571a659ba1d07ef507cd0cbdb1a6287e3320a3607b8a222a
Transactions (2)
Coinbasee30e39b5d1ad6a…62166f47171c24
1 in β†’ 1 out10.0600 XPM110 B
AeKNrjNj…1NEq95Ta
26add5c64cfed2…cb33a918dd610c
1 in β†’ 2 out7.9095 XPM227 B
AYoXsP48…NHHLdNAqATy1ugWs…K7Xo6g33
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.

6.218 Γ— 10⁹⁴(95-digit number)
62183812099370002868…49646845951743268440
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
6.218 Γ— 10⁹⁴(95-digit number)
62183812099370002868…49646845951743268441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.243 Γ— 10⁹⁡(96-digit number)
12436762419874000573…99293691903486536881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.487 Γ— 10⁹⁡(96-digit number)
24873524839748001147…98587383806973073761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.974 Γ— 10⁹⁡(96-digit number)
49747049679496002294…97174767613946147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.949 Γ— 10⁹⁡(96-digit number)
99494099358992004589…94349535227892295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.989 Γ— 10⁹⁢(97-digit number)
19898819871798400917…88699070455784590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.979 Γ— 10⁹⁢(97-digit number)
39797639743596801835…77398140911569180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.959 Γ— 10⁹⁢(97-digit number)
79595279487193603671…54796281823138360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.591 Γ— 10⁹⁷(98-digit number)
15919055897438720734…09592563646276720641
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 277715

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 23a677fe4704bf9d281e45b4467fe4e940fdb750291aa8b8741b5d024b56f6cc

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 #277,715 on Chainz β†—
Circulating Supply:57,892,093 XPMΒ·at block #6,830,993 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy