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Block #152,994

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 5:12:36 PM Β· Difficulty 9.8627 Β· 6,659,232 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b6cf52850beb640d47a819107769ed8f9f91ce7aa61474fcaf3876859128d7e
View on Chainz β†—

Height

#152,994

Difficulty

9.862666

Transactions

1

Size

199 B

Version

2

Bits

09dcd7af

Nonce

15,563

Timestamp

9/6/2013, 5:12:36 PM

Confirmations

6,659,232

Mined by

⛏️ P2SHARzKAGFyC84BWrrsxzVJMjM6R6E5bJQ6Gf

Merkle Root

60d4bfce680789a2e882b7f2f5b6b4350e2e829c83c3282be51ca46ede92af6f
Transactions (1)
Coinbase60d4bfce680789…1ca46ede92af6f
1 in β†’ 1 out10.2700 XPM109 B
ARzKAGFy…E5bJQ6Gf
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.

1.334 Γ— 10⁹⁡(96-digit number)
13344169605277001626…70858394437485102079
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
1.334 Γ— 10⁹⁡(96-digit number)
13344169605277001626…70858394437485102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.668 Γ— 10⁹⁡(96-digit number)
26688339210554003253…41716788874970204159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.337 Γ— 10⁹⁡(96-digit number)
53376678421108006507…83433577749940408319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁢(97-digit number)
10675335684221601301…66867155499880816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.135 Γ— 10⁹⁢(97-digit number)
21350671368443202602…33734310999761633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.270 Γ— 10⁹⁢(97-digit number)
42701342736886405205…67468621999523266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.540 Γ— 10⁹⁢(97-digit number)
85402685473772810411…34937243999046533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.708 Γ— 10⁹⁷(98-digit number)
17080537094754562082…69874487998093066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.416 Γ— 10⁹⁷(98-digit number)
34161074189509124164…39748975996186132479
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:57,741,823 XPMΒ·at block #6,812,225 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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