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Block #563,659

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/27/2014, 2:40:39 AM Β· Difficulty 10.9648 Β· 6,248,396 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3108d1d740abf853ef3cfee540888bb26798a967f86df86921912a4908a5ae93
View on Chainz β†—

Height

#563,659

Difficulty

10.964798

Transactions

1

Size

208 B

Version

2

Bits

0af6fd05

Nonce

923,674,963

Timestamp

5/27/2014, 2:40:39 AM

Confirmations

6,248,396

Merkle Root

6a2e0e80a2b25d38c53e24c34efcab820f4ed8d3c3ad2a2c3f31e96aacb9c569
Transactions (1)
Coinbase6a2e0e80a2b25d…31e96aacb9c569
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.

1.202 Γ— 10⁹⁹(100-digit number)
12027491829171722126…03915013908216305920
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
1.202 Γ— 10⁹⁹(100-digit number)
12027491829171722126…03915013908216305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.405 Γ— 10⁹⁹(100-digit number)
24054983658343444252…07830027816432611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.810 Γ— 10⁹⁹(100-digit number)
48109967316686888504…15660055632865223679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.621 Γ— 10⁹⁹(100-digit number)
96219934633373777009…31320111265730447359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.924 Γ— 10¹⁰⁰(101-digit number)
19243986926674755401…62640222531460894719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.848 Γ— 10¹⁰⁰(101-digit number)
38487973853349510803…25280445062921789439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.697 Γ— 10¹⁰⁰(101-digit number)
76975947706699021607…50560890125843578879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.539 Γ— 10¹⁰¹(102-digit number)
15395189541339804321…01121780251687157759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.079 Γ— 10¹⁰¹(102-digit number)
30790379082679608642…02243560503374315519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.158 Γ— 10¹⁰¹(102-digit number)
61580758165359217285…04487121006748631039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.231 Γ— 10¹⁰²(103-digit number)
12316151633071843457…08974242013497262079
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 563659

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 3108d1d740abf853ef3cfee540888bb26798a967f86df86921912a4908a5ae93

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 #563,659 on Chainz β†—
Circulating Supply:57,740,546 XPMΒ·at block #6,812,054 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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