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Block #920,191

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2015, 6:52:14 PM Β· Difficulty 10.9186 Β· 5,890,822 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91935581ed891c0e2b81cbc4911cde7f2413e8a4bdcf4fb38b21991f0d7ce8a0
View on Chainz β†—

Height

#920,191

Difficulty

10.918629

Transactions

2

Size

15.46 KB

Version

2

Bits

0aeb2b4b

Nonce

107,747,630

Timestamp

2/2/2015, 6:52:14 PM

Confirmations

5,890,822

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b12bb80bdef2324fc93c60d599c741725e78cd746666fb19860f1d3c7a0c8d33
Transactions (2)
Coinbase88fa1a14e29f38…d1e0ea82eac977
1 in β†’ 1 out8.5300 XPM116 B
ANSXnLY2…Sd25TjkD
2693c1c0dbe23e…60f8594688e4a4
105 in β†’ 2 out3480.0856 XPM15.26 KB
AYqJDmdZ…gKwhw8GSAZvtG9GA…mM2vbWwC
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.

3.839 Γ— 10⁹⁴(95-digit number)
38391074088440724782…39819910209977814571
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
3.839 Γ— 10⁹⁴(95-digit number)
38391074088440724782…39819910209977814571
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.678 Γ— 10⁹⁴(95-digit number)
76782148176881449564…79639820419955629141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.535 Γ— 10⁹⁡(96-digit number)
15356429635376289912…59279640839911258281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.071 Γ— 10⁹⁡(96-digit number)
30712859270752579825…18559281679822516561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.142 Γ— 10⁹⁡(96-digit number)
61425718541505159651…37118563359645033121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.228 Γ— 10⁹⁢(97-digit number)
12285143708301031930…74237126719290066241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.457 Γ— 10⁹⁢(97-digit number)
24570287416602063860…48474253438580132481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.914 Γ— 10⁹⁢(97-digit number)
49140574833204127721…96948506877160264961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.828 Γ— 10⁹⁢(97-digit number)
98281149666408255442…93897013754320529921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.965 Γ— 10⁹⁷(98-digit number)
19656229933281651088…87794027508641059841
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:57,732,209 XPMΒ·at block #6,811,012 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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