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Block #249,341

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2013, 9:59:34 PM Β· Difficulty 9.9667 Β· 6,547,537 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d44f5c6ba535e72dadfe59adc2161bcddc2c6c8e6c191ff2817203c825dbef6f
View on Chainz β†—

Height

#249,341

Difficulty

9.966738

Transactions

1

Size

231 B

Version

2

Bits

09f77c1f

Nonce

7,700

Timestamp

11/7/2013, 9:59:34 PM

Confirmations

6,547,537

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

33955dfcace033c78d141ca731bdd5fbb98f20c3e2648b4fc423f5768bedb51c
Transactions (1)
Coinbase33955dfcace033…23f5768bedb51c
1 in β†’ 2 out10.0500 XPM141 B
AKcbk49N…GJbKa7j1AKNbfPoc…jfkpwAyL
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.

6.585 Γ— 10⁹⁴(95-digit number)
65855683170660962971…34678636028526001699
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
6.585 Γ— 10⁹⁴(95-digit number)
65855683170660962971…34678636028526001699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁡(96-digit number)
13171136634132192594…69357272057052003399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.634 Γ— 10⁹⁡(96-digit number)
26342273268264385188…38714544114104006799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.268 Γ— 10⁹⁡(96-digit number)
52684546536528770376…77429088228208013599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.053 Γ— 10⁹⁢(97-digit number)
10536909307305754075…54858176456416027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.107 Γ— 10⁹⁢(97-digit number)
21073818614611508150…09716352912832054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.214 Γ— 10⁹⁢(97-digit number)
42147637229223016301…19432705825664108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.429 Γ— 10⁹⁢(97-digit number)
84295274458446032603…38865411651328217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.685 Γ— 10⁹⁷(98-digit number)
16859054891689206520…77730823302656435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.371 Γ— 10⁹⁷(98-digit number)
33718109783378413041…55461646605312870399
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:57,619,040 XPMΒ·at block #6,796,877 Β· updates every 60s
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