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Block #547,513

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2014, 12:47:10 PM Β· Difficulty 10.9572 Β· 6,269,242 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79b6871790b0379edfdbb0ec4f2fbff74bd5aab1712d00a5ca5c3f74b8a6f5a0
View on Chainz β†—

Height

#547,513

Difficulty

10.957223

Transactions

1

Size

201 B

Version

2

Bits

0af50c98

Nonce

56,639,626

Timestamp

5/16/2014, 12:47:10 PM

Confirmations

6,269,242

Mined by

⛏️ P2SHAXbupbytcwoNqw4M35pdUYCttowrUtPCrn

Merkle Root

1861b08fc8c6c7cf1c210c58b628a5552667adcec2ea13737fc19ce2f3f8c5e9
Transactions (1)
Coinbase1861b08fc8c6c7…c19ce2f3f8c5e9
1 in β†’ 1 out8.3200 XPM110 B
AXbupbyt…wrUtPCrn
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.

1.981 Γ— 10⁹⁷(98-digit number)
19812060558559443895…15189319456747381761
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.981 Γ— 10⁹⁷(98-digit number)
19812060558559443895…15189319456747381761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.962 Γ— 10⁹⁷(98-digit number)
39624121117118887790…30378638913494763521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.924 Γ— 10⁹⁷(98-digit number)
79248242234237775580…60757277826989527041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.584 Γ— 10⁹⁸(99-digit number)
15849648446847555116…21514555653979054081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.169 Γ— 10⁹⁸(99-digit number)
31699296893695110232…43029111307958108161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.339 Γ— 10⁹⁸(99-digit number)
63398593787390220464…86058222615916216321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.267 Γ— 10⁹⁹(100-digit number)
12679718757478044092…72116445231832432641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.535 Γ— 10⁹⁹(100-digit number)
25359437514956088185…44232890463664865281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.071 Γ— 10⁹⁹(100-digit number)
50718875029912176371…88465780927329730561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.014 Γ— 10¹⁰⁰(101-digit number)
10143775005982435274…76931561854659461121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.028 Γ— 10¹⁰⁰(101-digit number)
20287550011964870548…53863123709318922241
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 Second 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.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,778,071 XPMΒ·at block #6,816,754 Β· updates every 60s
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