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Block #901,686

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/19/2015, 6:50:46 PM Β· Difficulty 10.9409 Β· 5,916,247 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1fa63241d15ce658404648b1498073cea21f40076badbd497051fb0eb40aeeb4
View on Chainz β†—

Height

#901,686

Difficulty

10.940927

Transactions

2

Size

1.29 KB

Version

2

Bits

0af0e09a

Nonce

597,546,858

Timestamp

1/19/2015, 6:50:46 PM

Confirmations

5,916,247

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f702af3221ba3150d8da3793206419636b727ed246421d4da1af78e31183dd05
Transactions (2)
Coinbase5df03a70310292…5cc80b5721eafc
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
cb9c897f348826…7da9aeccf703eb
7 in β†’ 2 out2025.3144 XPM1.09 KB
AcAFW717…V1pWEX3JATPZjoTC…gHnRkVyW
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.

5.420 Γ— 10⁹⁡(96-digit number)
54203312318811742381…42455111171592101759
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
5.420 Γ— 10⁹⁡(96-digit number)
54203312318811742381…42455111171592101759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁢(97-digit number)
10840662463762348476…84910222343184203519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.168 Γ— 10⁹⁢(97-digit number)
21681324927524696952…69820444686368407039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.336 Γ— 10⁹⁢(97-digit number)
43362649855049393905…39640889372736814079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.672 Γ— 10⁹⁢(97-digit number)
86725299710098787811…79281778745473628159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁷(98-digit number)
17345059942019757562…58563557490947256319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.469 Γ— 10⁹⁷(98-digit number)
34690119884039515124…17127114981894512639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.938 Γ— 10⁹⁷(98-digit number)
69380239768079030248…34254229963789025279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁸(99-digit number)
13876047953615806049…68508459927578050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁸(99-digit number)
27752095907231612099…37016919855156101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.550 Γ— 10⁹⁸(99-digit number)
55504191814463224199…74033839710312202239
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:57,787,529 XPMΒ·at block #6,817,932 Β· updates every 60s
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