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Block #1,692,267

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2016, 5:50:22 AM Β· Difficulty 10.6847 Β· 5,148,616 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9fdc2f500d83908c29c5904a07a71403f2c547502f737e3fb9d705714fd097f1
View on Chainz β†—

Height

#1,692,267

Difficulty

10.684726

Transactions

1

Size

200 B

Version

2

Bits

0aaf4a33

Nonce

148,952,707

Timestamp

7/28/2016, 5:50:22 AM

Confirmations

5,148,616

Mined by

⛏️ P2SHAL1JuUC8masLu9fruc8ksZMqPSBG4srUvL

Merkle Root

69e552226229d68ebbb230d1fac8045d16ba4563e45215184438781a0ce5af06
Transactions (1)
Coinbase69e552226229d6…38781a0ce5af06
1 in β†’ 1 out8.7500 XPM109 B
AL1JuUC8…BG4srUvL
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.

4.253 Γ— 10⁹⁢(97-digit number)
42537272558062843797…94394990984340249599
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.253 Γ— 10⁹⁢(97-digit number)
42537272558062843797…94394990984340249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.507 Γ— 10⁹⁢(97-digit number)
85074545116125687595…88789981968680499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁷(98-digit number)
17014909023225137519…77579963937360998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.402 Γ— 10⁹⁷(98-digit number)
34029818046450275038…55159927874721996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.805 Γ— 10⁹⁷(98-digit number)
68059636092900550076…10319855749443993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.361 Γ— 10⁹⁸(99-digit number)
13611927218580110015…20639711498887987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.722 Γ— 10⁹⁸(99-digit number)
27223854437160220030…41279422997775974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.444 Γ— 10⁹⁸(99-digit number)
54447708874320440061…82558845995551948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁹(100-digit number)
10889541774864088012…65117691991103897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.177 Γ— 10⁹⁹(100-digit number)
21779083549728176024…30235383982207795199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,971,413 XPMΒ·at block #6,840,882 Β· updates every 60s
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