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Block #3,054,794

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/16/2019, 3:18:12 AM Β· Difficulty 11.0017 Β· 3,781,891 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a6cbfa632105952ff8dda62d20fdc774fa9f2b17a9c14749175053508a496ea
View on Chainz β†—

Height

#3,054,794

Difficulty

11.001720

Transactions

2

Size

1.14 KB

Version

2

Bits

0b0070c1

Nonce

368,924,583

Timestamp

2/16/2019, 3:18:12 AM

Confirmations

3,781,891

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

0a062459475ea3b3ca300c9fdaae7a85656ec2517deb943065787082ffacdad4
Transactions (2)
Coinbaseb5fd06037aff45…b05f35557c74f8
1 in β†’ 1 out8.2700 XPM110 B
AbXwmGxD…4XXYP765
120766f00caad0…f7eba135f9e924
6 in β†’ 2 out998.0000 XPM966 B
AXk8gZSJ…DA9sFG6wAaLK1SAe…sBd2eoHQ
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.

7.581 Γ— 10⁹³(94-digit number)
75812491602387583651…95758049256477605541
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
7.581 Γ— 10⁹³(94-digit number)
75812491602387583651…95758049256477605541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.516 Γ— 10⁹⁴(95-digit number)
15162498320477516730…91516098512955211081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.032 Γ— 10⁹⁴(95-digit number)
30324996640955033460…83032197025910422161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.064 Γ— 10⁹⁴(95-digit number)
60649993281910066921…66064394051820844321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.212 Γ— 10⁹⁡(96-digit number)
12129998656382013384…32128788103641688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.425 Γ— 10⁹⁡(96-digit number)
24259997312764026768…64257576207283377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.851 Γ— 10⁹⁡(96-digit number)
48519994625528053536…28515152414566754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.703 Γ— 10⁹⁡(96-digit number)
97039989251056107073…57030304829133509121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.940 Γ— 10⁹⁢(97-digit number)
19407997850211221414…14060609658267018241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.881 Γ— 10⁹⁢(97-digit number)
38815995700422442829…28121219316534036481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.763 Γ— 10⁹⁢(97-digit number)
77631991400844885659…56242438633068072961
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:57,937,761 XPMΒ·at block #6,836,684 Β· updates every 60s
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