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Block #446,855

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/16/2014, 8:55:47 PM Β· Difficulty 10.3596 Β· 6,354,403 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db657c414cd072991e789e762eb50c1deb0e07da8fdb2516f2d1cbe604deaa90
View on Chainz β†—

Height

#446,855

Difficulty

10.359604

Transactions

1

Size

201 B

Version

2

Bits

0a5c0efd

Nonce

240,608

Timestamp

3/16/2014, 8:55:47 PM

Confirmations

6,354,403

Merkle Root

2c258c326bc71ffc7bd2ecdd1d92e3c8a0014796765a7f5e880b21dcbc53748d
Transactions (1)
Coinbase2c258c326bc71f…0b21dcbc53748d
1 in β†’ 1 out9.3000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

4.518 Γ— 10⁹⁷(98-digit number)
45183298232035262754…19684997797310045530
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
4.518 Γ— 10⁹⁷(98-digit number)
45183298232035262754…19684997797310045529
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.036 Γ— 10⁹⁷(98-digit number)
90366596464070525509…39369995594620091059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.807 Γ— 10⁹⁸(99-digit number)
18073319292814105101…78739991189240182119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.614 Γ— 10⁹⁸(99-digit number)
36146638585628210203…57479982378480364239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.229 Γ— 10⁹⁸(99-digit number)
72293277171256420407…14959964756960728479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.445 Γ— 10⁹⁹(100-digit number)
14458655434251284081…29919929513921456959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.891 Γ— 10⁹⁹(100-digit number)
28917310868502568163…59839859027842913919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.783 Γ— 10⁹⁹(100-digit number)
57834621737005136326…19679718055685827839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.156 Γ— 10¹⁰⁰(101-digit number)
11566924347401027265…39359436111371655679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.313 Γ— 10¹⁰⁰(101-digit number)
23133848694802054530…78718872222743311359
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 446855

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 db657c414cd072991e789e762eb50c1deb0e07da8fdb2516f2d1cbe604deaa90

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 #446,855 on Chainz β†—
Circulating Supply:57,654,133 XPMΒ·at block #6,801,257 Β· updates every 60s
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