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Block #260,550

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/14/2013, 10:17:46 AM Β· Difficulty 9.9772 Β· 6,549,246 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cc76dc1b48cfeba914576c589d203652b0b88c5ba4156df4b022f2baa8757d7
View on Chainz β†—

Height

#260,550

Difficulty

9.977188

Transactions

1

Size

200 B

Version

2

Bits

09fa28fd

Nonce

92,388

Timestamp

11/14/2013, 10:17:46 AM

Confirmations

6,549,246

Mined by

⛏️ P2SHAbJsT1MFiTkk7HZiVSZy3MgHLJpF3oUXHW

Merkle Root

e1ca749f24ff2831b44a667639ba1659e38a12f2b5c62e99cc5ee26a8d3198e9
Transactions (1)
Coinbasee1ca749f24ff28…5ee26a8d3198e9
1 in β†’ 1 out10.0300 XPM109 B
AbJsT1MF…pF3oUXHW
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.

8.698 Γ— 10⁹⁡(96-digit number)
86989513054777674831…49686441061144678399
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
8.698 Γ— 10⁹⁡(96-digit number)
86989513054777674831…49686441061144678399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.739 Γ— 10⁹⁢(97-digit number)
17397902610955534966…99372882122289356799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.479 Γ— 10⁹⁢(97-digit number)
34795805221911069932…98745764244578713599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.959 Γ— 10⁹⁢(97-digit number)
69591610443822139865…97491528489157427199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.391 Γ— 10⁹⁷(98-digit number)
13918322088764427973…94983056978314854399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.783 Γ— 10⁹⁷(98-digit number)
27836644177528855946…89966113956629708799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.567 Γ— 10⁹⁷(98-digit number)
55673288355057711892…79932227913259417599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁸(99-digit number)
11134657671011542378…59864455826518835199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.226 Γ— 10⁹⁸(99-digit number)
22269315342023084756…19728911653037670399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.453 Γ— 10⁹⁸(99-digit number)
44538630684046169513…39457823306075340799
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:57,722,448 XPMΒ·at block #6,809,795 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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