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Block #148,896

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 12:49:15 AM Β· Difficulty 9.8560 Β· 6,653,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
20f1b1aced40d2835a5c3bc55174b67d30ba91303ce191214d352b3ee3b4f131
View on Chainz β†—

Height

#148,896

Difficulty

9.855956

Transactions

1

Size

199 B

Version

2

Bits

09db1ff4

Nonce

40,345

Timestamp

9/4/2013, 12:49:15 AM

Confirmations

6,653,601

Mined by

⛏️ P2SHAP91QEDQfufBUohT6sogfnRJN9W6JZAB9n

Merkle Root

f8821e087510acf19c81944a9c088a019dfacbc875fe1a04326ef7939eb94d2f
Transactions (1)
Coinbasef8821e087510ac…6ef7939eb94d2f
1 in β†’ 1 out10.2800 XPM109 B
AP91QEDQ…W6JZAB9n
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.

4.363 Γ— 10⁹⁴(95-digit number)
43632454420064324737…65101426976516724479
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
4.363 Γ— 10⁹⁴(95-digit number)
43632454420064324737…65101426976516724479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.726 Γ— 10⁹⁴(95-digit number)
87264908840128649474…30202853953033448959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.745 Γ— 10⁹⁡(96-digit number)
17452981768025729894…60405707906066897919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.490 Γ— 10⁹⁡(96-digit number)
34905963536051459789…20811415812133795839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.981 Γ— 10⁹⁡(96-digit number)
69811927072102919579…41622831624267591679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.396 Γ— 10⁹⁢(97-digit number)
13962385414420583915…83245663248535183359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.792 Γ— 10⁹⁢(97-digit number)
27924770828841167831…66491326497070366719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.584 Γ— 10⁹⁢(97-digit number)
55849541657682335663…32982652994140733439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁷(98-digit number)
11169908331536467132…65965305988281466879
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:57,663,984 XPMΒ·at block #6,802,496 Β· updates every 60s
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