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Block #413,442

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/21/2014, 6:07:25 AM Β· Difficulty 10.4141 Β· 6,396,814 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3443e0b817b77b82fbe8113c7bb17994ecf47cbdd5bb068c907c233bba24f4c4
View on Chainz β†—

Height

#413,442

Difficulty

10.414141

Transactions

1

Size

200 B

Version

2

Bits

0a6a052a

Nonce

58,715

Timestamp

2/21/2014, 6:07:25 AM

Confirmations

6,396,814

Mined by

⛏️ P2SHANNQjLEpZ4WgsDvFZ5dNRmaLdVGddva1Pt

Merkle Root

a2d03fd0cb04d91af4b527994835d30a9dcc5285be8e33633d39ab921c8acb25
Transactions (1)
Coinbasea2d03fd0cb04d9…39ab921c8acb25
1 in β†’ 1 out9.2100 XPM109 B
ANNQjLEp…Gddva1Pt
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.

8.808 Γ— 10⁹⁷(98-digit number)
88085876708034841870…46997666571876449699
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
8.808 Γ— 10⁹⁷(98-digit number)
88085876708034841870…46997666571876449699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁸(99-digit number)
17617175341606968374…93995333143752899399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.523 Γ— 10⁹⁸(99-digit number)
35234350683213936748…87990666287505798799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.046 Γ— 10⁹⁸(99-digit number)
70468701366427873496…75981332575011597599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.409 Γ— 10⁹⁹(100-digit number)
14093740273285574699…51962665150023195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.818 Γ— 10⁹⁹(100-digit number)
28187480546571149398…03925330300046390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.637 Γ— 10⁹⁹(100-digit number)
56374961093142298796…07850660600092780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.127 Γ— 10¹⁰⁰(101-digit number)
11274992218628459759…15701321200185561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.254 Γ— 10¹⁰⁰(101-digit number)
22549984437256919518…31402642400371123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.509 Γ— 10¹⁰⁰(101-digit number)
45099968874513839037…62805284800742246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.019 Γ— 10¹⁰⁰(101-digit number)
90199937749027678075…25610569601484492799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,726,121 XPMΒ·at block #6,810,255 Β· updates every 60s
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