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Block #209,689

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2013, 5:12:54 PM Β· Difficulty 9.9108 Β· 6,597,013 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f922fd1665ae6648a7f93477b932f6bbc491dde2b4952c57af34e4e4b2e8839c
View on Chainz β†—

Height

#209,689

Difficulty

9.910770

Transactions

1

Size

198 B

Version

2

Bits

09e9283b

Nonce

33,482

Timestamp

10/14/2013, 5:12:54 PM

Confirmations

6,597,013

Mined by

⛏️ P2SHAbERMcutQDScg9DXkU4LAqx7CDQQKtkzeK

Merkle Root

5d0d74bdd4826bcef6f456063c8dbca86976e32a12d2c77f1bbe3e330488b7b7
Transactions (1)
Coinbase5d0d74bdd4826b…be3e330488b7b7
1 in β†’ 1 out10.1700 XPM109 B
AbERMcut…QQKtkzeK
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.

2.974 Γ— 10⁹²(93-digit number)
29743094708308202244…27515339534080370669
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
2.974 Γ— 10⁹²(93-digit number)
29743094708308202244…27515339534080370669
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.948 Γ— 10⁹²(93-digit number)
59486189416616404489…55030679068160741339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.189 Γ— 10⁹³(94-digit number)
11897237883323280897…10061358136321482679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.379 Γ— 10⁹³(94-digit number)
23794475766646561795…20122716272642965359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.758 Γ— 10⁹³(94-digit number)
47588951533293123591…40245432545285930719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.517 Γ— 10⁹³(94-digit number)
95177903066586247183…80490865090571861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁴(95-digit number)
19035580613317249436…60981730181143722879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.807 Γ— 10⁹⁴(95-digit number)
38071161226634498873…21963460362287445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.614 Γ— 10⁹⁴(95-digit number)
76142322453268997746…43926920724574891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁡(96-digit number)
15228464490653799549…87853841449149783039
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:57,697,713 XPMΒ·at block #6,806,701 Β· updates every 60s
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