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Block #29,190

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 2:41:43 PM Β· Difficulty 7.9840 Β· 6,795,786 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9df4c6eb7cd2f44e42daf92e40717c8061003ac4c08d77fa33cba8edca6e9796
View on Chainz β†—

Height

#29,190

Difficulty

7.983998

Transactions

1

Size

200 B

Version

2

Bits

07fbe74e

Nonce

460

Timestamp

7/13/2013, 2:41:43 PM

Confirmations

6,795,786

Merkle Root

a9481b6c7e475fede14f20dfe4dafb0900435c22b291dcaa39ed781c6f30c162
Transactions (1)
Coinbasea9481b6c7e475f…ed781c6f30c162
1 in β†’ 1 out15.6700 XPM109 B
AanMCgWJ…3r4KGwHG
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.

1.387 Γ— 10⁹⁢(97-digit number)
13878288181492863336…18406818359275332520
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.387 Γ— 10⁹⁢(97-digit number)
13878288181492863336…18406818359275332519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁢(97-digit number)
27756576362985726673…36813636718550665039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.551 Γ— 10⁹⁢(97-digit number)
55513152725971453347…73627273437101330079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁷(98-digit number)
11102630545194290669…47254546874202660159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁷(98-digit number)
22205261090388581339…94509093748405320319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.441 Γ— 10⁹⁷(98-digit number)
44410522180777162678…89018187496810640639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.882 Γ— 10⁹⁷(98-digit number)
88821044361554325356…78036374993621281279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.776 Γ— 10⁹⁸(99-digit number)
17764208872310865071…56072749987242562559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the First 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 8
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 29190

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 9df4c6eb7cd2f44e42daf92e40717c8061003ac4c08d77fa33cba8edca6e9796

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 #29,190 on Chainz β†—
Circulating Supply:57,843,889 XPMΒ·at block #6,824,975 Β· updates every 60s
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