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Block #358,587

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/14/2014, 5:13:12 AM Β· Difficulty 10.3848 Β· 6,451,375 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f49205549b329458df7b2b10688602d0db577ad359fded5b3128bdbb7050fcdd
View on Chainz β†—

Height

#358,587

Difficulty

10.384753

Transactions

1

Size

200 B

Version

2

Bits

0a627f2f

Nonce

27,717

Timestamp

1/14/2014, 5:13:12 AM

Confirmations

6,451,375

Mined by

⛏️ P2SHAXKgkkDGrogBEHJHSetHJnSBPfJyE5mk6Y

Merkle Root

a4dd182fe40ce617323fa58cd7ce01435253842aaec334504ed3045d0dfc5bb0
Transactions (1)
Coinbasea4dd182fe40ce6…d3045d0dfc5bb0
1 in β†’ 1 out9.2600 XPM109 B
AXKgkkDG…JyE5mk6Y
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.

1.553 Γ— 10⁹⁸(99-digit number)
15539220311382276120…70719624699908927479
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
1.553 Γ— 10⁹⁸(99-digit number)
15539220311382276120…70719624699908927479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.107 Γ— 10⁹⁸(99-digit number)
31078440622764552241…41439249399817854959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.215 Γ— 10⁹⁸(99-digit number)
62156881245529104483…82878498799635709919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.243 Γ— 10⁹⁹(100-digit number)
12431376249105820896…65756997599271419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.486 Γ— 10⁹⁹(100-digit number)
24862752498211641793…31513995198542839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.972 Γ— 10⁹⁹(100-digit number)
49725504996423283586…63027990397085679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.945 Γ— 10⁹⁹(100-digit number)
99451009992846567172…26055980794171358719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.989 Γ— 10¹⁰⁰(101-digit number)
19890201998569313434…52111961588342717439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.978 Γ— 10¹⁰⁰(101-digit number)
39780403997138626869…04223923176685434879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.956 Γ— 10¹⁰⁰(101-digit number)
79560807994277253738…08447846353370869759
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,723,768 XPMΒ·at block #6,809,961 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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