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Block #2,133,050

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 5:40:20 AM Β· Difficulty 10.9101 Β· 4,709,808 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22e1432d7289f50c3c239d41417f0c3f342ec109193ea5c45611816642dba72f
View on Chainz β†—

Height

#2,133,050

Difficulty

10.910110

Transactions

1

Size

199 B

Version

2

Bits

0ae8fcf3

Nonce

1,807,675,891

Timestamp

5/26/2017, 5:40:20 AM

Confirmations

4,709,808

Mined by

⛏️ P2SHAYXRMkAVKbCoVUuq3KPkRtSfVYNeEYstaF

Merkle Root

656994c0bdc9fb0737ee5996dbf7d17c553875928fb4622267b5db22fc0cc026
Transactions (1)
Coinbase656994c0bdc9fb…b5db22fc0cc026
1 in β†’ 1 out8.3900 XPM109 B
AYXRMkAV…NeEYstaF
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.

3.806 Γ— 10⁹³(94-digit number)
38067664783005627925…79696336008588522881
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
3.806 Γ— 10⁹³(94-digit number)
38067664783005627925…79696336008588522881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.613 Γ— 10⁹³(94-digit number)
76135329566011255851…59392672017177045761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.522 Γ— 10⁹⁴(95-digit number)
15227065913202251170…18785344034354091521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.045 Γ— 10⁹⁴(95-digit number)
30454131826404502340…37570688068708183041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.090 Γ— 10⁹⁴(95-digit number)
60908263652809004681…75141376137416366081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.218 Γ— 10⁹⁡(96-digit number)
12181652730561800936…50282752274832732161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.436 Γ— 10⁹⁡(96-digit number)
24363305461123601872…00565504549665464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.872 Γ— 10⁹⁡(96-digit number)
48726610922247203744…01131009099330928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.745 Γ— 10⁹⁡(96-digit number)
97453221844494407489…02262018198661857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.949 Γ— 10⁹⁢(97-digit number)
19490644368898881497…04524036397323714561
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:57,987,211 XPMΒ·at block #6,842,857 Β· updates every 60s
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