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Block #2,762,111

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2018, 8:45:10 PM Β· Difficulty 11.6555 Β· 4,068,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0991a7b30bb48088a7430a385ec93325584c3a3947a1f391f472c9c1df7f390d
View on Chainz β†—

Height

#2,762,111

Difficulty

11.655461

Transactions

2

Size

1.28 KB

Version

2

Bits

0ba7cc52

Nonce

32,421,127

Timestamp

7/23/2018, 8:45:10 PM

Confirmations

4,068,532

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

9b416a33e97347b4ffefcc3347f663434775eb61a0373808c23a131d9dfd7cf8
Transactions (2)
Coinbase66a6abc7dc896a…45bcf0b037bcd0
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
ba9f35f4e70f38…80de6945b94dc9
7 in β†’ 2 out209.8691 XPM1.09 KB
Aa17Jz7u…uDM1g79xAbiZw7N1…HPacQJfk
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.

4.423 Γ— 10⁹⁡(96-digit number)
44231320206548532517…64590318332134420481
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
4.423 Γ— 10⁹⁡(96-digit number)
44231320206548532517…64590318332134420481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.846 Γ— 10⁹⁡(96-digit number)
88462640413097065034…29180636664268840961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.769 Γ— 10⁹⁢(97-digit number)
17692528082619413006…58361273328537681921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.538 Γ— 10⁹⁢(97-digit number)
35385056165238826013…16722546657075363841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.077 Γ— 10⁹⁢(97-digit number)
70770112330477652027…33445093314150727681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.415 Γ— 10⁹⁷(98-digit number)
14154022466095530405…66890186628301455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.830 Γ— 10⁹⁷(98-digit number)
28308044932191060811…33780373256602910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.661 Γ— 10⁹⁷(98-digit number)
56616089864382121622…67560746513205821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.132 Γ— 10⁹⁸(99-digit number)
11323217972876424324…35121493026411642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.264 Γ— 10⁹⁸(99-digit number)
22646435945752848648…70242986052823285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.529 Γ— 10⁹⁸(99-digit number)
45292871891505697297…40485972105646571521
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:57,889,269 XPMΒ·at block #6,830,642 Β· updates every 60s
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