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Block #920,344

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2015, 9:26:16 PM Β· Difficulty 10.9186 Β· 5,886,142 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9d36bad611e93f5ddc53c19ccb18e45dcc2c49bfea80b1a2485453ea7697d33
View on Chainz β†—

Height

#920,344

Difficulty

10.918627

Transactions

2

Size

9.67 KB

Version

2

Bits

0aeb2b27

Nonce

1,075,762,278

Timestamp

2/2/2015, 9:26:16 PM

Confirmations

5,886,142

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cadea6af1dc3c3c6f0ace581e905d8062e3a29e230db55bd97433bb51c7161e7
Transactions (2)
Coinbase881c4e55924366…7f8ae4d6599c65
1 in β†’ 1 out8.4700 XPM116 B
ANSXnLY2…Sd25TjkD
57d1109fb4b359…5e29add25c2907
65 in β†’ 2 out1999.9100 XPM9.47 KB
ANB1x9fy…xabUg7z7Ab5F14cB…BshbDJcB
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.

1.010 Γ— 10⁹⁢(97-digit number)
10108630267394119020…37388622472748784401
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
1.010 Γ— 10⁹⁢(97-digit number)
10108630267394119020…37388622472748784401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.021 Γ— 10⁹⁢(97-digit number)
20217260534788238041…74777244945497568801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.043 Γ— 10⁹⁢(97-digit number)
40434521069576476082…49554489890995137601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.086 Γ— 10⁹⁢(97-digit number)
80869042139152952165…99108979781990275201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.617 Γ— 10⁹⁷(98-digit number)
16173808427830590433…98217959563980550401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.234 Γ— 10⁹⁷(98-digit number)
32347616855661180866…96435919127961100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.469 Γ— 10⁹⁷(98-digit number)
64695233711322361732…92871838255922201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.293 Γ— 10⁹⁸(99-digit number)
12939046742264472346…85743676511844403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.587 Γ— 10⁹⁸(99-digit number)
25878093484528944692…71487353023688806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.175 Γ— 10⁹⁸(99-digit number)
51756186969057889385…42974706047377612801
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,695,981 XPMΒ·at block #6,806,485 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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