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Block #1,568,547

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2016, 8:03:34 AM Β· Difficulty 10.7586 Β· 5,265,081 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28c23e24ee0c3ce0434b335b8c8dd62d7b27f76714f561a942e398a3e110ec58
View on Chainz β†—

Difficulty

10.758629

Transactions

1

Size

200 B

Version

2

Bits

0ac2357f

Nonce

15,032,406

Timestamp

5/2/2016, 8:03:34 AM

Confirmations

5,265,081

Merkle Root

3e0094a56562dedd30047b5fae57b3b78e23e4a86aff984a8266078e562b89e4
Transactions (1)
Coinbase3e0094a56562de…66078e562b89e4
1 in β†’ 1 out8.6300 XPM110 B
ATHaCv1e…9cAEc7f8
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.

3.364 Γ— 10⁹⁴(95-digit number)
33648400573925322183…64687138657125928160
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
3.364 Γ— 10⁹⁴(95-digit number)
33648400573925322183…64687138657125928159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.729 Γ— 10⁹⁴(95-digit number)
67296801147850644366…29374277314251856319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.345 Γ— 10⁹⁡(96-digit number)
13459360229570128873…58748554628503712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.691 Γ— 10⁹⁡(96-digit number)
26918720459140257746…17497109257007425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.383 Γ— 10⁹⁡(96-digit number)
53837440918280515493…34994218514014850559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁢(97-digit number)
10767488183656103098…69988437028029701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.153 Γ— 10⁹⁢(97-digit number)
21534976367312206197…39976874056059402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.306 Γ— 10⁹⁢(97-digit number)
43069952734624412394…79953748112118804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.613 Γ— 10⁹⁢(97-digit number)
86139905469248824788…59907496224237608959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.722 Γ— 10⁹⁷(98-digit number)
17227981093849764957…19814992448475217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.445 Γ— 10⁹⁷(98-digit number)
34455962187699529915…39629984896950435839
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 1568547

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 28c23e24ee0c3ce0434b335b8c8dd62d7b27f76714f561a942e398a3e110ec58

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 #1,568,547 on Chainz β†—
Circulating Supply:57,913,234 XPMΒ·at block #6,833,627 Β· updates every 60s
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