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Block #49,029

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 6:16:22 PM Β· Difficulty 8.8571 Β· 6,756,637 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb19abd985228e00f77cbd7e6612460960c0de4191695f31b12d352e4ccc39c5
View on Chainz β†—

Height

#49,029

Difficulty

8.857093

Transactions

1

Size

200 B

Version

2

Bits

08db6a6c

Nonce

564

Timestamp

7/15/2013, 6:16:22 PM

Confirmations

6,756,637

Merkle Root

07442bfcd8a1c9317be7298238c21b6238d0e5edfcddd0bef78bdb110776f3d2
Transactions (1)
Coinbase07442bfcd8a1c9…8bdb110776f3d2
1 in β†’ 1 out12.7300 XPM110 B
AQJsQ7PY…G9pNZ1RN
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.

5.331 Γ— 10⁹⁴(95-digit number)
53315741205678683565…49888457996157647400
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
5.331 Γ— 10⁹⁴(95-digit number)
53315741205678683565…49888457996157647401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.066 Γ— 10⁹⁡(96-digit number)
10663148241135736713…99776915992315294801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.132 Γ— 10⁹⁡(96-digit number)
21326296482271473426…99553831984630589601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.265 Γ— 10⁹⁡(96-digit number)
42652592964542946852…99107663969261179201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.530 Γ— 10⁹⁡(96-digit number)
85305185929085893705…98215327938522358401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.706 Γ— 10⁹⁢(97-digit number)
17061037185817178741…96430655877044716801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.412 Γ— 10⁹⁢(97-digit number)
34122074371634357482…92861311754089433601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.824 Γ— 10⁹⁢(97-digit number)
68244148743268714964…85722623508178867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.364 Γ— 10⁹⁷(98-digit number)
13648829748653742992…71445247016357734401
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 49029

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 cb19abd985228e00f77cbd7e6612460960c0de4191695f31b12d352e4ccc39c5

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 #49,029 on Chainz β†—
Circulating Supply:57,689,406 XPMΒ·at block #6,805,665 Β· updates every 60s
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