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Block #533,385

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2014, 4:27:10 PM Β· Difficulty 10.8995 Β· 6,307,425 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b43ab196a6116298b6e2a453290827e69298aa4ff0e9ab1b77b0fa252d7ecc72
View on Chainz β†—

Height

#533,385

Difficulty

10.899490

Transactions

1

Size

201 B

Version

2

Bits

0ae644ff

Nonce

1,381,524,620

Timestamp

5/9/2014, 4:27:10 PM

Confirmations

6,307,425

Mined by

⛏️ P2SHAWgU9gnbngA9ETy7qc4tJzv2RSfEJUnY3P

Merkle Root

dedeb255353208a511d623b68952bde3fa7c4c0cafea526e420234eb61217b31
Transactions (1)
Coinbasededeb255353208…0234eb61217b31
1 in β†’ 1 out8.4000 XPM112 B
AWgU9gnb…fEJUnY3P
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.

2.661 Γ— 10⁹¹(92-digit number)
26615224746645007747…45149098395233177271
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
2.661 Γ— 10⁹¹(92-digit number)
26615224746645007747…45149098395233177271
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.323 Γ— 10⁹¹(92-digit number)
53230449493290015494…90298196790466354541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.064 Γ— 10⁹²(93-digit number)
10646089898658003098…80596393580932709081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.129 Γ— 10⁹²(93-digit number)
21292179797316006197…61192787161865418161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.258 Γ— 10⁹²(93-digit number)
42584359594632012395…22385574323730836321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.516 Γ— 10⁹²(93-digit number)
85168719189264024791…44771148647461672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.703 Γ— 10⁹³(94-digit number)
17033743837852804958…89542297294923345281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.406 Γ— 10⁹³(94-digit number)
34067487675705609916…79084594589846690561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.813 Γ— 10⁹³(94-digit number)
68134975351411219832…58169189179693381121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.362 Γ— 10⁹⁴(95-digit number)
13626995070282243966…16338378359386762241
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:57,970,830 XPMΒ·at block #6,840,809 Β· updates every 60s
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