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Block #135,353

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 2:05:07 PM Β· Difficulty 9.8100 Β· 6,666,881 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9cbe0d97c97342e552c3ccac6fa5a6729758818dc4854c16af2bb2396d0a6217
View on Chainz β†—

Height

#135,353

Difficulty

9.810006

Transactions

1

Size

203 B

Version

2

Bits

09cf5c8e

Nonce

743,906

Timestamp

8/26/2013, 2:05:07 PM

Confirmations

6,666,881

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

ade6d9b26ad582ba7d8918e1e7f04560af4df5d55acfe0b1913b40c9289c0593
Transactions (1)
Coinbaseade6d9b26ad582…3b40c9289c0593
1 in β†’ 1 out10.3800 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.505 Γ— 10⁹⁸(99-digit number)
25059820893195023896…68541795359347823989
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
2.505 Γ— 10⁹⁸(99-digit number)
25059820893195023896…68541795359347823989
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.011 Γ— 10⁹⁸(99-digit number)
50119641786390047792…37083590718695647979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁹(100-digit number)
10023928357278009558…74167181437391295959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.004 Γ— 10⁹⁹(100-digit number)
20047856714556019117…48334362874782591919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.009 Γ— 10⁹⁹(100-digit number)
40095713429112038234…96668725749565183839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.019 Γ— 10⁹⁹(100-digit number)
80191426858224076468…93337451499130367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.603 Γ— 10¹⁰⁰(101-digit number)
16038285371644815293…86674902998260735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.207 Γ— 10¹⁰⁰(101-digit number)
32076570743289630587…73349805996521470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.415 Γ— 10¹⁰⁰(101-digit number)
64153141486579261174…46699611993042941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.283 Γ— 10¹⁰¹(102-digit number)
12830628297315852234…93399223986085882879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,661,880 XPMΒ·at block #6,802,233 Β· updates every 60s
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