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Block #1,611,230

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2016, 4:52:21 PM Β· Difficulty 10.6068 Β· 5,233,526 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
54153ca3f73ab03360bd0fadc90730175590325fd4e1859a56ced729aecea81a
View on Chainz β†—

Height

#1,611,230

Difficulty

10.606811

Transactions

1

Size

200 B

Version

2

Bits

0a9b57fc

Nonce

1,736,496,418

Timestamp

6/2/2016, 4:52:21 PM

Confirmations

5,233,526

Mined by

⛏️ P2SHAQ6uc3NqXF8pKPrFjSYXviJBzKauda8bi8

Merkle Root

673c6d4439b9d081c5e52d6ac80b40923ece63ce0b6c7bdf9d833e3bb706d596
Transactions (1)
Coinbase673c6d4439b9d0…833e3bb706d596
1 in β†’ 1 out8.8700 XPM109 B
AQ6uc3Nq…auda8bi8
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.

9.700 Γ— 10⁹⁡(96-digit number)
97002177560551641750…73108337810022404479
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
9.700 Γ— 10⁹⁡(96-digit number)
97002177560551641750…73108337810022404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.940 Γ— 10⁹⁢(97-digit number)
19400435512110328350…46216675620044808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.880 Γ— 10⁹⁢(97-digit number)
38800871024220656700…92433351240089617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.760 Γ— 10⁹⁢(97-digit number)
77601742048441313400…84866702480179235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.552 Γ— 10⁹⁷(98-digit number)
15520348409688262680…69733404960358471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.104 Γ— 10⁹⁷(98-digit number)
31040696819376525360…39466809920716943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.208 Γ— 10⁹⁷(98-digit number)
62081393638753050720…78933619841433886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.241 Γ— 10⁹⁸(99-digit number)
12416278727750610144…57867239682867773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.483 Γ— 10⁹⁸(99-digit number)
24832557455501220288…15734479365735546879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.966 Γ— 10⁹⁸(99-digit number)
49665114911002440576…31468958731471093759
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:58,002,463 XPMΒ·at block #6,844,755 Β· updates every 60s
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