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Block #669,463

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2014, 10:38:27 PM Β· Difficulty 10.9639 Β· 6,156,090 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8536c363832b596ceac81f92fd685c38433fe9ec1a73dddad99f4e120d33d062
View on Chainz β†—

Height

#669,463

Difficulty

10.963867

Transactions

2

Size

434 B

Version

2

Bits

0af6bff5

Nonce

625,032,403

Timestamp

8/8/2014, 10:38:27 PM

Confirmations

6,156,090

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bc89c3320df2b14ecbc6aec09ef49b3430773225e22de3679634384324d0bf0b
Transactions (2)
Coinbase3760a4bc001217…01f5dc4bddfdd4
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
6f1d8c9fe07d57…39f4f0d7f56e68
1 in β†’ 2 out6.0622 XPM226 B
AHjoz3Pg…qv9ARwXeAJsznj81…o2EqYfFD
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.

4.449 Γ— 10⁹⁹(100-digit number)
44494620962498160992…23667014129256273919
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
4.449 Γ— 10⁹⁹(100-digit number)
44494620962498160992…23667014129256273919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.898 Γ— 10⁹⁹(100-digit number)
88989241924996321984…47334028258512547839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.779 Γ— 10¹⁰⁰(101-digit number)
17797848384999264396…94668056517025095679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.559 Γ— 10¹⁰⁰(101-digit number)
35595696769998528793…89336113034050191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.119 Γ— 10¹⁰⁰(101-digit number)
71191393539997057587…78672226068100382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.423 Γ— 10¹⁰¹(102-digit number)
14238278707999411517…57344452136200765439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.847 Γ— 10¹⁰¹(102-digit number)
28476557415998823035…14688904272401530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.695 Γ— 10¹⁰¹(102-digit number)
56953114831997646070…29377808544803061759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.139 Γ— 10¹⁰²(103-digit number)
11390622966399529214…58755617089606123519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.278 Γ— 10¹⁰²(103-digit number)
22781245932799058428…17511234179212247039
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:57,848,525 XPMΒ·at block #6,825,552 Β· updates every 60s
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