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Block #894,589

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/14/2015, 6:39:14 AM Β· Difficulty 10.9498 Β· 5,910,684 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
200612cbcd935351958e07e2e73bd3f926b8a6eeaa3bb710324bbf9b6d95870d
View on Chainz β†—

Height

#894,589

Difficulty

10.949800

Transactions

2

Size

878 B

Version

2

Bits

0af32615

Nonce

1,212,268,261

Timestamp

1/14/2015, 6:39:14 AM

Confirmations

5,910,684

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1667d99a1ec7ade6ced0731130156c3bc47f0f8b8d9b1abe601c4922101478d6
Transactions (2)
Coinbasec8ba1b58668821…3354787bcd20d3
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
f1b2f5f4767e87…bd152700a2e505
4 in β†’ 2 out2716.4267 XPM671 B
ALBXoLU2…cJbmz2JHAQUC7Hue…LL2XMoNY
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.

1.206 Γ— 10⁹⁸(99-digit number)
12066738343304551001…33465866387342602239
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
1.206 Γ— 10⁹⁸(99-digit number)
12066738343304551001…33465866387342602239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.413 Γ— 10⁹⁸(99-digit number)
24133476686609102003…66931732774685204479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.826 Γ— 10⁹⁸(99-digit number)
48266953373218204006…33863465549370408959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.653 Γ— 10⁹⁸(99-digit number)
96533906746436408013…67726931098740817919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.930 Γ— 10⁹⁹(100-digit number)
19306781349287281602…35453862197481635839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.861 Γ— 10⁹⁹(100-digit number)
38613562698574563205…70907724394963271679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.722 Γ— 10⁹⁹(100-digit number)
77227125397149126410…41815448789926543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.544 Γ— 10¹⁰⁰(101-digit number)
15445425079429825282…83630897579853086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.089 Γ— 10¹⁰⁰(101-digit number)
30890850158859650564…67261795159706173439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.178 Γ— 10¹⁰⁰(101-digit number)
61781700317719301128…34523590319412346879
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:57,686,255 XPMΒ·at block #6,805,272 Β· updates every 60s
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