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Block #670,485

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2014, 3:04:30 PM Β· Difficulty 10.9642 Β· 6,138,994 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
776ffbe4ea06edc19b158e69244a87e12f4530f177eb7a4c5b0285720508d67e
View on Chainz β†—

Height

#670,485

Difficulty

10.964161

Transactions

2

Size

876 B

Version

2

Bits

0af6d340

Nonce

29,901,409

Timestamp

8/9/2014, 3:04:30 PM

Confirmations

6,138,994

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

356fe20e0f3f525ed7ea746b8fc6cff205fa0b461a1ae415d35906850b1de7e9
Transactions (2)
Coinbase9dbe6293d08624…79adf348993376
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
2a2f929fb34779…f73ba846600e7a
4 in β†’ 2 out274.9100 XPM669 B
ATP6ihBz…va7MpWW8AZ8HHXPz…EhReJjLk
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.

4.678 Γ— 10⁹⁢(97-digit number)
46786165905225084044…25548425807072912319
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
4.678 Γ— 10⁹⁢(97-digit number)
46786165905225084044…25548425807072912319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.357 Γ— 10⁹⁢(97-digit number)
93572331810450168088…51096851614145824639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.871 Γ— 10⁹⁷(98-digit number)
18714466362090033617…02193703228291649279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.742 Γ— 10⁹⁷(98-digit number)
37428932724180067235…04387406456583298559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.485 Γ— 10⁹⁷(98-digit number)
74857865448360134470…08774812913166597119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.497 Γ— 10⁹⁸(99-digit number)
14971573089672026894…17549625826333194239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.994 Γ— 10⁹⁸(99-digit number)
29943146179344053788…35099251652666388479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.988 Γ— 10⁹⁸(99-digit number)
59886292358688107576…70198503305332776959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.197 Γ— 10⁹⁹(100-digit number)
11977258471737621515…40397006610665553919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.395 Γ— 10⁹⁹(100-digit number)
23954516943475243030…80794013221331107839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.790 Γ— 10⁹⁹(100-digit number)
47909033886950486061…61588026442662215679
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:57,719,902 XPMΒ·at block #6,809,478 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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