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Block #401,651

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/12/2014, 10:05:56 PM Β· Difficulty 10.4339 Β· 6,423,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5302a3995e3a6652b6035ea7e2c2bd28f8d9792afcaa1936131439223930ef12
View on Chainz β†—

Height

#401,651

Difficulty

10.433931

Transactions

1

Size

202 B

Version

2

Bits

0a6f1615

Nonce

308,783

Timestamp

2/12/2014, 10:05:56 PM

Confirmations

6,423,557

Merkle Root

d932438ce622bb9cbdcc95a711f870c4c18f12a20e4796d943356c5339d07e24
Transactions (1)
Coinbased932438ce622bb…356c5339d07e24
1 in β†’ 1 out9.1700 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.

2.572 Γ— 10⁹⁸(99-digit number)
25724690687461357212…81667257634965834520
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
2.572 Γ— 10⁹⁸(99-digit number)
25724690687461357212…81667257634965834519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.144 Γ— 10⁹⁸(99-digit number)
51449381374922714424…63334515269931669039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁹(100-digit number)
10289876274984542884…26669030539863338079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁹(100-digit number)
20579752549969085769…53338061079726676159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.115 Γ— 10⁹⁹(100-digit number)
41159505099938171539…06676122159453352319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.231 Γ— 10⁹⁹(100-digit number)
82319010199876343078…13352244318906704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.646 Γ— 10¹⁰⁰(101-digit number)
16463802039975268615…26704488637813409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.292 Γ— 10¹⁰⁰(101-digit number)
32927604079950537231…53408977275626818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.585 Γ— 10¹⁰⁰(101-digit number)
65855208159901074462…06817954551253637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.317 Γ— 10¹⁰¹(102-digit number)
13171041631980214892…13635909102507274239
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 401651

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 5302a3995e3a6652b6035ea7e2c2bd28f8d9792afcaa1936131439223930ef12

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 #401,651 on Chainz β†—
Circulating Supply:57,845,758 XPMΒ·at block #6,825,207 Β· updates every 60s
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