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Block #555,618

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2014, 4:35:05 PM Β· Difficulty 10.9629 Β· 6,248,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9581c7e0854d858f217f824c563f98e88b887a6b042b2b5b53d10af593eae989
View on Chainz β†—

Height

#555,618

Difficulty

10.962861

Transactions

2

Size

399 B

Version

2

Bits

0af67e0c

Nonce

192,476,213

Timestamp

5/21/2014, 4:35:05 PM

Confirmations

6,248,596

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2c1a259a00c213a7ef2368347b7d5ee6e221dcc66bda06242cb43e8e392233b0
Transactions (2)
Coinbaseb591b95d34766d…efc8ae8d4418d3
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
a9c4dbcd9ab80e…4249be2bbc6b32
1 in β†’ 2 out8.3000 XPM192 B
AL9UZuKj…g3Q3eciVAeKNrjNj…1NEq95Ta
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.

8.069 Γ— 10⁹⁷(98-digit number)
80697767712574829525…11826180235874206159
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
8.069 Γ— 10⁹⁷(98-digit number)
80697767712574829525…11826180235874206159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.613 Γ— 10⁹⁸(99-digit number)
16139553542514965905…23652360471748412319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.227 Γ— 10⁹⁸(99-digit number)
32279107085029931810…47304720943496824639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.455 Γ— 10⁹⁸(99-digit number)
64558214170059863620…94609441886993649279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.291 Γ— 10⁹⁹(100-digit number)
12911642834011972724…89218883773987298559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.582 Γ— 10⁹⁹(100-digit number)
25823285668023945448…78437767547974597119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.164 Γ— 10⁹⁹(100-digit number)
51646571336047890896…56875535095949194239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.032 Γ— 10¹⁰⁰(101-digit number)
10329314267209578179…13751070191898388479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.065 Γ— 10¹⁰⁰(101-digit number)
20658628534419156358…27502140383796776959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.131 Γ— 10¹⁰⁰(101-digit number)
41317257068838312716…55004280767593553919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.263 Γ— 10¹⁰⁰(101-digit number)
82634514137676625433…10008561535187107839
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:57,677,760 XPMΒ·at block #6,804,213 Β· updates every 60s
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