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Block #643,338

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2014, 9:23:07 AM Β· Difficulty 10.9564 Β· 6,161,864 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c46e9fdf91bb5387e8e1f2b9cb2ea58db44bff8d3a72bc981312e4b853767d5
View on Chainz β†—

Height

#643,338

Difficulty

10.956436

Transactions

2

Size

434 B

Version

2

Bits

0af4d8ff

Nonce

1,192,345,404

Timestamp

7/22/2014, 9:23:07 AM

Confirmations

6,161,864

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1960e2f518f7fed574bcd23e49a742a2a39d7464df2175e89b9d8eec0229016d
Transactions (2)
Coinbase0eb7402826421b…baa854645e7222
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
7740979ed107f8…9ddc83eb417184
1 in β†’ 2 out441.7608 XPM227 B
AQ5BdQBC…d6gJriKLARMmjyvz…4PLUTMJK
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.

5.442 Γ— 10⁹⁷(98-digit number)
54425013017540752629…83140184951654758401
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
5.442 Γ— 10⁹⁷(98-digit number)
54425013017540752629…83140184951654758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.088 Γ— 10⁹⁸(99-digit number)
10885002603508150525…66280369903309516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.177 Γ— 10⁹⁸(99-digit number)
21770005207016301051…32560739806619033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.354 Γ— 10⁹⁸(99-digit number)
43540010414032602103…65121479613238067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.708 Γ— 10⁹⁸(99-digit number)
87080020828065204206…30242959226476134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.741 Γ— 10⁹⁹(100-digit number)
17416004165613040841…60485918452952268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.483 Γ— 10⁹⁹(100-digit number)
34832008331226081682…20971836905904537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.966 Γ— 10⁹⁹(100-digit number)
69664016662452163365…41943673811809075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.393 Γ— 10¹⁰⁰(101-digit number)
13932803332490432673…83887347623618150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.786 Γ— 10¹⁰⁰(101-digit number)
27865606664980865346…67774695247236300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.573 Γ— 10¹⁰⁰(101-digit number)
55731213329961730692…35549390494472601601
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:57,685,687 XPMΒ·at block #6,805,201 Β· updates every 60s
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