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Block #912,893

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/28/2015, 6:50:53 AM Β· Difficulty 10.9279 Β· 5,886,545 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ba5467c15d39e03c92f763aa843f7048d5591d8b78e2b83448f691808860e16
View on Chainz β†—

Height

#912,893

Difficulty

10.927890

Transactions

2

Size

3.89 KB

Version

2

Bits

0aed8a32

Nonce

474,143,344

Timestamp

1/28/2015, 6:50:53 AM

Confirmations

5,886,545

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

454b962efdd7f6f7839dca62c78e1254ba442e5a76c91d7f66354412279dde9f
Transactions (2)
Coinbase9f5e2307e56f1b…ae36e6ea48ebaf
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
7d783fd76dbf4a…4b06f09acf3882
25 in β†’ 2 out1722.9006 XPM3.69 KB
AYUhjfE6…v73yrZHCAcAFW717…V1pWEX3J
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.

1.785 Γ— 10⁹⁸(99-digit number)
17857850470972603925…98924951990953738239
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
1.785 Γ— 10⁹⁸(99-digit number)
17857850470972603925…98924951990953738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.571 Γ— 10⁹⁸(99-digit number)
35715700941945207850…97849903981907476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.143 Γ— 10⁹⁸(99-digit number)
71431401883890415700…95699807963814952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.428 Γ— 10⁹⁹(100-digit number)
14286280376778083140…91399615927629905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.857 Γ— 10⁹⁹(100-digit number)
28572560753556166280…82799231855259811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.714 Γ— 10⁹⁹(100-digit number)
57145121507112332560…65598463710519623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.142 Γ— 10¹⁰⁰(101-digit number)
11429024301422466512…31196927421039247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.285 Γ— 10¹⁰⁰(101-digit number)
22858048602844933024…62393854842078494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.571 Γ— 10¹⁰⁰(101-digit number)
45716097205689866048…24787709684156989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.143 Γ— 10¹⁰⁰(101-digit number)
91432194411379732096…49575419368313978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.828 Γ— 10¹⁰¹(102-digit number)
18286438882275946419…99150838736627957759
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:57,639,555 XPMΒ·at block #6,799,437 Β· updates every 60s
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