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Block #577,881

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/5/2014, 3:22:28 PM Β· Difficulty 10.9685 Β· 6,248,283 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9e0e40dcffe1c701118cb7018063c6ac8ac795800776a38c7c45c8dbe56f354a
View on Chainz β†—

Height

#577,881

Difficulty

10.968545

Transactions

1

Size

207 B

Version

2

Bits

0af7f298

Nonce

448,762,276

Timestamp

6/5/2014, 3:22:28 PM

Confirmations

6,248,283

Merkle Root

663c192031a30024f9342f26d8442e2436008079d174cbb83d8c33b58f27ec75
Transactions (1)
Coinbase663c192031a300…8c33b58f27ec75
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.

2.437 Γ— 10⁹⁷(98-digit number)
24373377564028414949…36455886344401071320
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
2.437 Γ— 10⁹⁷(98-digit number)
24373377564028414949…36455886344401071319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.874 Γ— 10⁹⁷(98-digit number)
48746755128056829898…72911772688802142639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.749 Γ— 10⁹⁷(98-digit number)
97493510256113659796…45823545377604285279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.949 Γ— 10⁹⁸(99-digit number)
19498702051222731959…91647090755208570559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.899 Γ— 10⁹⁸(99-digit number)
38997404102445463918…83294181510417141119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.799 Γ— 10⁹⁸(99-digit number)
77994808204890927837…66588363020834282239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.559 Γ— 10⁹⁹(100-digit number)
15598961640978185567…33176726041668564479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.119 Γ— 10⁹⁹(100-digit number)
31197923281956371134…66353452083337128959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.239 Γ— 10⁹⁹(100-digit number)
62395846563912742269…32706904166674257919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.247 Γ— 10¹⁰⁰(101-digit number)
12479169312782548453…65413808333348515839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.495 Γ— 10¹⁰⁰(101-digit number)
24958338625565096907…30827616666697031679
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 577881

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 9e0e40dcffe1c701118cb7018063c6ac8ac795800776a38c7c45c8dbe56f354a

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 #577,881 on Chainz β†—
Circulating Supply:57,853,439 XPMΒ·at block #6,826,163 Β· updates every 60s
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