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Block #561,284

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/25/2014, 11:01:51 AM Β· Difficulty 10.9648 Β· 6,265,924 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ba3de57c4da6dcdfc94067136dcc2cae87e09f92040b2685a78e870d60d2e1f
View on Chainz β†—

Height

#561,284

Difficulty

10.964751

Transactions

1

Size

243 B

Version

2

Bits

0af6f9f1

Nonce

375,736,299

Timestamp

5/25/2014, 11:01:51 AM

Confirmations

6,265,924

Merkle Root

81add6bec6ce6aa3441fd299fea0e2e7c030792466d461fd16aacd307d3a77a7
Transactions (1)
Coinbase81add6bec6ce6a…aacd307d3a77a7
1 in β†’ 2 out8.3000 XPM152 B
AKBQKQ1u…CKKLJCCJALPu3s2c…EJXLjVFh
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.

8.199 Γ— 10⁹⁷(98-digit number)
81992436888259951495…78386026676376874040
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
8.199 Γ— 10⁹⁷(98-digit number)
81992436888259951495…78386026676376874039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.639 Γ— 10⁹⁸(99-digit number)
16398487377651990299…56772053352753748079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.279 Γ— 10⁹⁸(99-digit number)
32796974755303980598…13544106705507496159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.559 Γ— 10⁹⁸(99-digit number)
65593949510607961196…27088213411014992319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.311 Γ— 10⁹⁹(100-digit number)
13118789902121592239…54176426822029984639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.623 Γ— 10⁹⁹(100-digit number)
26237579804243184478…08352853644059969279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.247 Γ— 10⁹⁹(100-digit number)
52475159608486368957…16705707288119938559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.049 Γ— 10¹⁰⁰(101-digit number)
10495031921697273791…33411414576239877119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.099 Γ— 10¹⁰⁰(101-digit number)
20990063843394547582…66822829152479754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.198 Γ— 10¹⁰⁰(101-digit number)
41980127686789095165…33645658304959508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.396 Γ— 10¹⁰⁰(101-digit number)
83960255373578190331…67291316609919016959
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 561284

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 2ba3de57c4da6dcdfc94067136dcc2cae87e09f92040b2685a78e870d60d2e1f

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 #561,284 on Chainz β†—
Circulating Supply:57,861,762 XPMΒ·at block #6,827,207 Β· updates every 60s
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