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Block #221,323

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2013, 12:30:55 PM Β· Difficulty 9.9386 Β· 6,583,956 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
802b53fc4fe7a03efa748db88452e3fc116a91f4815d5873a196b68e2cc3b85e
View on Chainz β†—

Height

#221,323

Difficulty

9.938607

Transactions

1

Size

205 B

Version

2

Bits

09f04887

Nonce

16,779,258

Timestamp

10/21/2013, 12:30:55 PM

Confirmations

6,583,956

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

1293eeefab237166d99b952445e9b273c5cb0cc249ad793e2a3cfedd0bb67584
Transactions (1)
Coinbase1293eeefab2371…3cfedd0bb67584
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.720 Γ— 10⁹²(93-digit number)
17201887511868935177…65009004974169903039
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
1.720 Γ— 10⁹²(93-digit number)
17201887511868935177…65009004974169903039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.440 Γ— 10⁹²(93-digit number)
34403775023737870354…30018009948339806079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.880 Γ— 10⁹²(93-digit number)
68807550047475740709…60036019896679612159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.376 Γ— 10⁹³(94-digit number)
13761510009495148141…20072039793359224319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.752 Γ— 10⁹³(94-digit number)
27523020018990296283…40144079586718448639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.504 Γ— 10⁹³(94-digit number)
55046040037980592567…80288159173436897279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁴(95-digit number)
11009208007596118513…60576318346873794559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.201 Γ— 10⁹⁴(95-digit number)
22018416015192237027…21152636693747589119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.403 Γ— 10⁹⁴(95-digit number)
44036832030384474054…42305273387495178239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.807 Γ— 10⁹⁴(95-digit number)
88073664060768948108…84610546774990356479
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:57,686,304 XPMΒ·at block #6,805,278 Β· updates every 60s
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