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Block #2,131,517

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 4:05:59 AM Β· Difficulty 10.9101 Β· 4,707,997 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
207e3dc12da6c2b506b83834850ec2362d56613ca92523f94221faff107c22a3
View on Chainz β†—

Height

#2,131,517

Difficulty

10.910062

Transactions

2

Size

1018 B

Version

2

Bits

0ae8f9d3

Nonce

696,856,121

Timestamp

5/25/2017, 4:05:59 AM

Confirmations

4,707,997

Mined by

⛏️ P2SHAZVzXwX43o77K49cKAcUqQtvL7p4h9jUsn

Merkle Root

8d03b80934123baf7e029e15a7eee4a4dbb139fb99f205ec53de63d0c4cde0b9
Transactions (2)
Coinbase0dbdb41e867e11…9228ee0281d425
1 in β†’ 1 out8.4000 XPM109 B
AZVzXwX4…p4h9jUsn
bc1ac353e081c2…6a91d8b20f34f9
5 in β†’ 2 out1539.9530 XPM820 B
ANBd6Bpg…E4fcbiDCAPQMSSnw…obgCN6eN
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.

3.693 Γ— 10⁹²(93-digit number)
36938336355196334366…50196486176951162401
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
3.693 Γ— 10⁹²(93-digit number)
36938336355196334366…50196486176951162401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.387 Γ— 10⁹²(93-digit number)
73876672710392668733…00392972353902324801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.477 Γ— 10⁹³(94-digit number)
14775334542078533746…00785944707804649601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.955 Γ— 10⁹³(94-digit number)
29550669084157067493…01571889415609299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.910 Γ— 10⁹³(94-digit number)
59101338168314134987…03143778831218598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.182 Γ— 10⁹⁴(95-digit number)
11820267633662826997…06287557662437196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.364 Γ— 10⁹⁴(95-digit number)
23640535267325653994…12575115324874393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.728 Γ— 10⁹⁴(95-digit number)
47281070534651307989…25150230649748787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.456 Γ— 10⁹⁴(95-digit number)
94562141069302615979…50300461299497574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.891 Γ— 10⁹⁡(96-digit number)
18912428213860523195…00600922598995148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.782 Γ— 10⁹⁡(96-digit number)
37824856427721046391…01201845197990297601
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
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