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Block #669,871

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2014, 4:57:01 AM Β· Difficulty 10.9641 Β· 6,166,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ee7a01fd2d7e093cc1d29823bf224393c5cd88e8568869bcce13945fd8dd0f9
View on Chainz β†—

Height

#669,871

Difficulty

10.964071

Transactions

2

Size

729 B

Version

2

Bits

0af6cd5a

Nonce

94,686,448

Timestamp

8/9/2014, 4:57:01 AM

Confirmations

6,166,642

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4c8931f53d5a900ac6fabe7b4771c7b0d8876448332f56989125378b60168468
Transactions (2)
Coinbasee1f3f3d5ed011c…3aa14f9cf53692
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
944bc6c9626434…41d3c18c8eafe0
3 in β†’ 2 out1352.9500 XPM523 B
ANpa33Ud…dtZZ7veKARseQQ6A…RPh9BxYP
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.

6.440 Γ— 10⁹⁡(96-digit number)
64404098401525421082…33907130438457965441
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.440 Γ— 10⁹⁡(96-digit number)
64404098401525421082…33907130438457965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.288 Γ— 10⁹⁢(97-digit number)
12880819680305084216…67814260876915930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.576 Γ— 10⁹⁢(97-digit number)
25761639360610168432…35628521753831861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.152 Γ— 10⁹⁢(97-digit number)
51523278721220336865…71257043507663723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.030 Γ— 10⁹⁷(98-digit number)
10304655744244067373…42514087015327447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.060 Γ— 10⁹⁷(98-digit number)
20609311488488134746…85028174030654894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.121 Γ— 10⁹⁷(98-digit number)
41218622976976269492…70056348061309788161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.243 Γ— 10⁹⁷(98-digit number)
82437245953952538985…40112696122619576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.648 Γ— 10⁹⁸(99-digit number)
16487449190790507797…80225392245239152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.297 Γ— 10⁹⁸(99-digit number)
32974898381581015594…60450784490478305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.594 Γ— 10⁹⁸(99-digit number)
65949796763162031188…20901568980956610561
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,936,381 XPMΒ·at block #6,836,512 Β· updates every 60s
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