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Block #293,754

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2013, 12:10:16 PM Β· Difficulty 9.9907 Β· 6,511,419 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4511c653291ea2923ee7ac993d734ae43f11d603362bca3c2873d0d2d0bcba0d
View on Chainz β†—

Height

#293,754

Difficulty

9.990743

Transactions

1

Size

207 B

Version

2

Bits

09fda153

Nonce

92,073

Timestamp

12/4/2013, 12:10:16 PM

Confirmations

6,511,419

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

0ac13f671135bd16cd1e6502ba5138ef1839e80e971f9cea14abfb23966eba16
Transactions (1)
Coinbase0ac13f671135bd…abfb23966eba16
1 in β†’ 1 out10.0000 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.

2.674 Γ— 10⁹⁷(98-digit number)
26748698846321583661…48492161312442713599
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
2.674 Γ— 10⁹⁷(98-digit number)
26748698846321583661…48492161312442713599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.349 Γ— 10⁹⁷(98-digit number)
53497397692643167323…96984322624885427199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁸(99-digit number)
10699479538528633464…93968645249770854399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.139 Γ— 10⁹⁸(99-digit number)
21398959077057266929…87937290499541708799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.279 Γ— 10⁹⁸(99-digit number)
42797918154114533859…75874580999083417599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.559 Γ— 10⁹⁸(99-digit number)
85595836308229067718…51749161998166835199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.711 Γ— 10⁹⁹(100-digit number)
17119167261645813543…03498323996333670399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.423 Γ— 10⁹⁹(100-digit number)
34238334523291627087…06996647992667340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.847 Γ— 10⁹⁹(100-digit number)
68476669046583254174…13993295985334681599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.369 Γ— 10¹⁰⁰(101-digit number)
13695333809316650834…27986591970669363199
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:57,685,452 XPMΒ·at block #6,805,172 Β· updates every 60s
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