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Block #563,106

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2014, 5:33:53 PM Β· Difficulty 10.9648 Β· 6,246,855 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
694ad9b3495fc1ea3f74ff40fd2265418c78081c88b6c63875f52bc293766f08
View on Chainz β†—

Height

#563,106

Difficulty

10.964764

Transactions

1

Size

208 B

Version

2

Bits

0af6face

Nonce

201,282,890

Timestamp

5/26/2014, 5:33:53 PM

Confirmations

6,246,855

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8447c06020b95b1d3c485f214cb319d9fa56544e9d85830ae0df2f7b1bc42cc0
Transactions (1)
Coinbase8447c06020b95b…df2f7b1bc42cc0
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.

3.248 Γ— 10⁹⁹(100-digit number)
32482189701937299452…55539784656588236801
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
3.248 Γ— 10⁹⁹(100-digit number)
32482189701937299452…55539784656588236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.496 Γ— 10⁹⁹(100-digit number)
64964379403874598904…11079569313176473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.299 Γ— 10¹⁰⁰(101-digit number)
12992875880774919780…22159138626352947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.598 Γ— 10¹⁰⁰(101-digit number)
25985751761549839561…44318277252705894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.197 Γ— 10¹⁰⁰(101-digit number)
51971503523099679123…88636554505411788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.039 Γ— 10¹⁰¹(102-digit number)
10394300704619935824…77273109010823577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.078 Γ— 10¹⁰¹(102-digit number)
20788601409239871649…54546218021647155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.157 Γ— 10¹⁰¹(102-digit number)
41577202818479743298…09092436043294310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.315 Γ— 10¹⁰¹(102-digit number)
83154405636959486597…18184872086588620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.663 Γ— 10¹⁰²(103-digit number)
16630881127391897319…36369744173177241601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,723,760 XPMΒ·at block #6,809,960 Β· updates every 60s
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