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Block #671,324

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/10/2014, 5:17:41 AM Β· Difficulty 10.9641 Β· 6,166,695 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7b765297f5ff76f260a750dbe9178970900e9a5d3d3a918f34400eb7a811e2f
View on Chainz β†—

Height

#671,324

Difficulty

10.964074

Transactions

1

Size

207 B

Version

2

Bits

0af6cd8d

Nonce

3,236,653,344

Timestamp

8/10/2014, 5:17:41 AM

Confirmations

6,166,695

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

523eca7f8ba1a37256bffdad0d09051f9d6cb24f24f13aa1ecf4748a0843af76
Transactions (1)
Coinbase523eca7f8ba1a3…f4748a0843af76
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.767 Γ— 10⁹⁢(97-digit number)
17677394565482518066…48089722161143051519
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
1.767 Γ— 10⁹⁢(97-digit number)
17677394565482518066…48089722161143051519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.535 Γ— 10⁹⁢(97-digit number)
35354789130965036132…96179444322286103039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.070 Γ— 10⁹⁢(97-digit number)
70709578261930072265…92358888644572206079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁷(98-digit number)
14141915652386014453…84717777289144412159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.828 Γ— 10⁹⁷(98-digit number)
28283831304772028906…69435554578288824319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.656 Γ— 10⁹⁷(98-digit number)
56567662609544057812…38871109156577648639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁸(99-digit number)
11313532521908811562…77742218313155297279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.262 Γ— 10⁹⁸(99-digit number)
22627065043817623124…55484436626310594559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.525 Γ— 10⁹⁸(99-digit number)
45254130087635246249…10968873252621189119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.050 Γ— 10⁹⁸(99-digit number)
90508260175270492499…21937746505242378239
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:57,948,506 XPMΒ·at block #6,838,018 Β· updates every 60s
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