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Block #2,158,370

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2017, 12:58:19 AM Β· Difficulty 10.9049 Β· 4,668,254 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0f460a5eef2526fc12e23d0516891d42f176367f560b9d72fe7b2bfbe104983
View on Chainz β†—

Height

#2,158,370

Difficulty

10.904935

Transactions

2

Size

3.05 KB

Version

2

Bits

0ae7a9cf

Nonce

687,730,486

Timestamp

6/13/2017, 12:58:19 AM

Confirmations

4,668,254

Mined by

⛏️ P2SHANe3tBY7h8v6xAps9Arv4WeRB5mbzUv9fq

Merkle Root

3303e1bff02cf426019514c525dc7fd509eed973867a734ea637db2dc78ab12a
Transactions (2)
Coinbase9592d178659093…3a10dc68124fbb
1 in β†’ 1 out8.4300 XPM109 B
ANe3tBY7…mbzUv9fq
d09a422f7907c5…64d527856ef1fe
19 in β†’ 3 out3626.6940 XPM2.86 KB
Ada1dx2w…8gd1gZg2ANxHW6qR…zqTa7HrPAZECtSGq…44ufCYHr
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.

5.946 Γ— 10⁹³(94-digit number)
59463662240576995313…97148942599056422701
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
5.946 Γ— 10⁹³(94-digit number)
59463662240576995313…97148942599056422701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.189 Γ— 10⁹⁴(95-digit number)
11892732448115399062…94297885198112845401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.378 Γ— 10⁹⁴(95-digit number)
23785464896230798125…88595770396225690801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.757 Γ— 10⁹⁴(95-digit number)
47570929792461596250…77191540792451381601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.514 Γ— 10⁹⁴(95-digit number)
95141859584923192501…54383081584902763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.902 Γ— 10⁹⁡(96-digit number)
19028371916984638500…08766163169805526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.805 Γ— 10⁹⁡(96-digit number)
38056743833969277000…17532326339611052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.611 Γ— 10⁹⁡(96-digit number)
76113487667938554001…35064652679222105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.522 Γ— 10⁹⁢(97-digit number)
15222697533587710800…70129305358444211201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.044 Γ— 10⁹⁢(97-digit number)
30445395067175421600…40258610716888422401
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:57,857,146 XPMΒ·at block #6,826,623 Β· updates every 60s
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