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Block #563,080

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2014, 5:10:46 PM Β· Difficulty 10.9647 Β· 6,236,494 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2cfcdb82e7115fbd9f4d99955c99c9347ed2b37324b29f768ab4dd32f0f2d317
View on Chainz β†—

Height

#563,080

Difficulty

10.964730

Transactions

1

Size

208 B

Version

2

Bits

0af6f88b

Nonce

826,215,319

Timestamp

5/26/2014, 5:10:46 PM

Confirmations

6,236,494

Merkle Root

e61e01704815019e39adaa4ce32acc19aff1c2642d5106cbcac9429773753dd1
Transactions (1)
Coinbasee61e0170481501…c9429773753dd1
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.875 Γ— 10⁹⁹(100-digit number)
28753810019380673546…07558522674312314880
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
2.875 Γ— 10⁹⁹(100-digit number)
28753810019380673546…07558522674312314879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.750 Γ— 10⁹⁹(100-digit number)
57507620038761347092…15117045348624629759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.150 Γ— 10¹⁰⁰(101-digit number)
11501524007752269418…30234090697249259519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.300 Γ— 10¹⁰⁰(101-digit number)
23003048015504538837…60468181394498519039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.600 Γ— 10¹⁰⁰(101-digit number)
46006096031009077674…20936362788997038079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.201 Γ— 10¹⁰⁰(101-digit number)
92012192062018155348…41872725577994076159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.840 Γ— 10¹⁰¹(102-digit number)
18402438412403631069…83745451155988152319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.680 Γ— 10¹⁰¹(102-digit number)
36804876824807262139…67490902311976304639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.360 Γ— 10¹⁰¹(102-digit number)
73609753649614524278…34981804623952609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.472 Γ— 10¹⁰²(103-digit number)
14721950729922904855…69963609247905218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.944 Γ— 10¹⁰²(103-digit number)
29443901459845809711…39927218495810437119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 563080

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 2cfcdb82e7115fbd9f4d99955c99c9347ed2b37324b29f768ab4dd32f0f2d317

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 #563,080 on Chainz β†—
Circulating Supply:57,640,641 XPMΒ·at block #6,799,573 Β· updates every 60s
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