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Block #151,930

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 11:48:15 PM Β· Difficulty 9.8621 Β· 6,654,072 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f64fd9aafb6a3adfddafa8b8ef464780b1e94ef6cd57260135daaef712493ac
View on Chainz β†—

Height

#151,930

Difficulty

9.862125

Transactions

1

Size

197 B

Version

2

Bits

09dcb437

Nonce

277,421

Timestamp

9/5/2013, 11:48:15 PM

Confirmations

6,654,072

Mined by

⛏️ P2SHAQDX4A7fYRFPkMLMMFvDCVebjcjoSW2gJw

Merkle Root

11c88dd565d04a15991ef3cb01e0bd1b24cd6d1d1aeda83e0b77860eb8b424b2
Transactions (1)
Coinbase11c88dd565d04a…77860eb8b424b2
1 in β†’ 1 out10.2700 XPM109 B
AQDX4A7f…joSW2gJw
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.

1.153 Γ— 10⁸⁹(90-digit number)
11535035708518976884…71090167604717676999
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
1.153 Γ— 10⁸⁹(90-digit number)
11535035708518976884…71090167604717676999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.307 Γ— 10⁸⁹(90-digit number)
23070071417037953769…42180335209435353999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.614 Γ— 10⁸⁹(90-digit number)
46140142834075907539…84360670418870707999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.228 Γ— 10⁸⁹(90-digit number)
92280285668151815078…68721340837741415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.845 Γ— 10⁹⁰(91-digit number)
18456057133630363015…37442681675482831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.691 Γ— 10⁹⁰(91-digit number)
36912114267260726031…74885363350965663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.382 Γ— 10⁹⁰(91-digit number)
73824228534521452063…49770726701931327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.476 Γ— 10⁹¹(92-digit number)
14764845706904290412…99541453403862655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.952 Γ— 10⁹¹(92-digit number)
29529691413808580825…99082906807725311999
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:57,692,093 XPMΒ·at block #6,806,001 Β· updates every 60s
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