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Home/Chain Registry/Block #1,429,735

Block #1,429,735

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/27/2016, 2:03:19 AM Β· Difficulty 10.7435 Β· 5,408,625 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b9102ad42b648892ece0c77cf43e69b4b20778106804a64f854336f2a895cfeb
View on Chainz β†—

Difficulty

10.743489

Transactions

1

Size

200 B

Version

2

Bits

0abe554c

Nonce

1,018,857,942

Timestamp

1/27/2016, 2:03:19 AM

Confirmations

5,408,625

Merkle Root

9e384de7084dd005bf4a38c39576571d9dfe9eeea217f84c28020a65fb5bc8a9
Transactions (1)
Coinbase9e384de7084dd0…020a65fb5bc8a9
1 in β†’ 1 out8.6500 XPM110 B
Ad3afPT5…rixfYFAH
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.

1.030 Γ— 10⁹⁴(95-digit number)
10308470298132208338…69711329741847900800
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
1.030 Γ— 10⁹⁴(95-digit number)
10308470298132208338…69711329741847900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.061 Γ— 10⁹⁴(95-digit number)
20616940596264416676…39422659483695801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.123 Γ— 10⁹⁴(95-digit number)
41233881192528833353…78845318967391603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.246 Γ— 10⁹⁴(95-digit number)
82467762385057666707…57690637934783206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁡(96-digit number)
16493552477011533341…15381275869566412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.298 Γ— 10⁹⁡(96-digit number)
32987104954023066683…30762551739132825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.597 Γ— 10⁹⁡(96-digit number)
65974209908046133366…61525103478265651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁢(97-digit number)
13194841981609226673…23050206956531302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.638 Γ— 10⁹⁢(97-digit number)
26389683963218453346…46100413913062604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.277 Γ— 10⁹⁢(97-digit number)
52779367926436906693…92200827826125209599
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 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
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 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 1429735

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 b9102ad42b648892ece0c77cf43e69b4b20778106804a64f854336f2a895cfeb

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 #1,429,735 on Chainz β†—
Circulating Supply:57,951,147 XPMΒ·at block #6,838,359 Β· updates every 60s
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