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Block #2,593,981

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/31/2018, 12:52:16 PM Β· Difficulty 11.3000 Β· 4,239,813 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c333880106f032d1b95ccb79b50d5a401588cf57430362a0aa6e462b55af4689
View on Chainz β†—

Height

#2,593,981

Difficulty

11.299982

Transactions

2

Size

78.19 KB

Version

2

Bits

0b4ccba6

Nonce

943,091,704

Timestamp

3/31/2018, 12:52:16 PM

Confirmations

4,239,813

Mined by

⛏️ P2SHAejdpFpsLTzp6YhrPFZe7tBzLy8pAvR3DX

Merkle Root

b936ccde43245c7d8d9775d056d585f5c79cd6e36c554574a284731d1653eeaf
Transactions (2)
Coinbasec59353ee9872c9…c6495a64067c95
1 in β†’ 1 out8.7400 XPM110 B
AejdpFps…8pAvR3DX
d7c3fab5812268…2b8ef3b5e5d133
539 in β†’ 2 out5000.0101 XPM77.99 KB
AK3pu9zg…F8C9Gfv8ALPF8J52…Hjw4BMsG
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.

1.113 Γ— 10⁹⁴(95-digit number)
11134413628278965496…66178215845416871321
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
1.113 Γ— 10⁹⁴(95-digit number)
11134413628278965496…66178215845416871321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.226 Γ— 10⁹⁴(95-digit number)
22268827256557930992…32356431690833742641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.453 Γ— 10⁹⁴(95-digit number)
44537654513115861984…64712863381667485281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.907 Γ— 10⁹⁴(95-digit number)
89075309026231723968…29425726763334970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.781 Γ— 10⁹⁡(96-digit number)
17815061805246344793…58851453526669941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.563 Γ— 10⁹⁡(96-digit number)
35630123610492689587…17702907053339882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.126 Γ— 10⁹⁡(96-digit number)
71260247220985379174…35405814106679764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.425 Γ— 10⁹⁢(97-digit number)
14252049444197075834…70811628213359528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.850 Γ— 10⁹⁢(97-digit number)
28504098888394151669…41623256426719057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.700 Γ— 10⁹⁢(97-digit number)
57008197776788303339…83246512853438115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.140 Γ— 10⁹⁷(98-digit number)
11401639555357660667…66493025706876231681
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:57,914,573 XPMΒ·at block #6,833,793 Β· updates every 60s
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