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Block #135,474

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 3:45:23 PM Β· Difficulty 9.8108 Β· 6,668,561 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16a9e4bacf16947f60715bf8eab686169a727a92c6207763234ba5e6da37fee4
View on Chainz β†—

Height

#135,474

Difficulty

9.810769

Transactions

1

Size

199 B

Version

2

Bits

09cf8e8a

Nonce

77,662

Timestamp

8/26/2013, 3:45:23 PM

Confirmations

6,668,561

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

f5e82bb18918085806eef1079c1db328a443ce4efec28ebaba3427d1c320cffa
Transactions (1)
Coinbasef5e82bb1891808…3427d1c320cffa
1 in β†’ 1 out10.3700 XPM109 B
Acecj4WY…wKtCNbS5
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.

6.756 Γ— 10⁹⁴(95-digit number)
67569350432306498069…22961935543406575999
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
6.756 Γ— 10⁹⁴(95-digit number)
67569350432306498069…22961935543406575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁡(96-digit number)
13513870086461299613…45923871086813151999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.702 Γ— 10⁹⁡(96-digit number)
27027740172922599227…91847742173626303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.405 Γ— 10⁹⁡(96-digit number)
54055480345845198455…83695484347252607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁢(97-digit number)
10811096069169039691…67390968694505215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.162 Γ— 10⁹⁢(97-digit number)
21622192138338079382…34781937389010431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.324 Γ— 10⁹⁢(97-digit number)
43244384276676158764…69563874778020863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.648 Γ— 10⁹⁢(97-digit number)
86488768553352317528…39127749556041727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.729 Γ— 10⁹⁷(98-digit number)
17297753710670463505…78255499112083455999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,676,332 XPMΒ·at block #6,804,034 Β· updates every 60s
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