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Block #552,682

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/19/2014, 3:37:46 PM Β· Difficulty 10.9628 Β· 6,259,964 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aac0456920cf526286dbc543cfa722cf6f986cb564bf312455f47c61b351e638
View on Chainz β†—

Height

#552,682

Difficulty

10.962768

Transactions

1

Size

244 B

Version

2

Bits

0af677fc

Nonce

805,575,449

Timestamp

5/19/2014, 3:37:46 PM

Confirmations

6,259,964

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

29b736f7e101d68189486be42fc8654be3dabcb99e7a669b5d7b611fb95f8cf5
Transactions (1)
Coinbase29b736f7e101d6…7b611fb95f8cf5
1 in β†’ 2 out8.3100 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
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.

3.677 Γ— 10⁹⁸(99-digit number)
36778870045510814786…90937689454207900879
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
3.677 Γ— 10⁹⁸(99-digit number)
36778870045510814786…90937689454207900879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.355 Γ— 10⁹⁸(99-digit number)
73557740091021629573…81875378908415801759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.471 Γ— 10⁹⁹(100-digit number)
14711548018204325914…63750757816831603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.942 Γ— 10⁹⁹(100-digit number)
29423096036408651829…27501515633663207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.884 Γ— 10⁹⁹(100-digit number)
58846192072817303658…55003031267326414079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.176 Γ— 10¹⁰⁰(101-digit number)
11769238414563460731…10006062534652828159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.353 Γ— 10¹⁰⁰(101-digit number)
23538476829126921463…20012125069305656319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.707 Γ— 10¹⁰⁰(101-digit number)
47076953658253842927…40024250138611312639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.415 Γ— 10¹⁰⁰(101-digit number)
94153907316507685854…80048500277222625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.883 Γ— 10¹⁰¹(102-digit number)
18830781463301537170…60097000554445250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.766 Γ— 10¹⁰¹(102-digit number)
37661562926603074341…20194001108890501119
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.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,745,196 XPMΒ·at block #6,812,645 Β· updates every 60s
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