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Block #1,597,207

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/23/2016, 10:07:26 PM Β· Difficulty 10.6112 Β· 5,245,570 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
32cc97325ddfd3db2295bd1a80ed92d3dac35ce11720758f6f8f5b457003b48d
View on Chainz β†—

Difficulty

10.611203

Transactions

1

Size

200 B

Version

2

Bits

0a9c77cc

Nonce

114,549,552

Timestamp

5/23/2016, 10:07:26 PM

Confirmations

5,245,570

Merkle Root

25abe416c7a07febc0891a282b6bbdeb7b020d504c04144065fea30cd1768049
Transactions (1)
Coinbase25abe416c7a07f…fea30cd1768049
1 in β†’ 1 out8.8700 XPM109 B
AWq8nLsy…pbJ1SoeS
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.

7.929 Γ— 10⁹⁢(97-digit number)
79296563766604038761…85432235664981135360
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
7.929 Γ— 10⁹⁢(97-digit number)
79296563766604038761…85432235664981135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.585 Γ— 10⁹⁷(98-digit number)
15859312753320807752…70864471329962270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.171 Γ— 10⁹⁷(98-digit number)
31718625506641615504…41728942659924541439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.343 Γ— 10⁹⁷(98-digit number)
63437251013283231009…83457885319849082879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁸(99-digit number)
12687450202656646201…66915770639698165759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.537 Γ— 10⁹⁸(99-digit number)
25374900405313292403…33831541279396331519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.074 Γ— 10⁹⁸(99-digit number)
50749800810626584807…67663082558792663039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁹(100-digit number)
10149960162125316961…35326165117585326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁹(100-digit number)
20299920324250633923…70652330235170652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁹(100-digit number)
40599840648501267846…41304660470341304319
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 1597207

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 32cc97325ddfd3db2295bd1a80ed92d3dac35ce11720758f6f8f5b457003b48d

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 #1,597,207 on Chainz β†—
Circulating Supply:57,986,555 XPMΒ·at block #6,842,776 Β· updates every 60s
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