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Block #169,937

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2013, 9:35:03 AM Β· Difficulty 9.8666 Β· 6,641,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e3e05af353656cb4d65fac1c8ebe5f3e98b207a7fd0442c6293aa2d08ddb48d
View on Chainz β†—

Height

#169,937

Difficulty

9.866615

Transactions

1

Size

198 B

Version

2

Bits

09ddda81

Nonce

65,603

Timestamp

9/18/2013, 9:35:03 AM

Confirmations

6,641,166

Mined by

⛏️ P2SHALSo2SoEeuC5J8GG2HeN1gyp2LvZXwVMRC

Merkle Root

fec7d62e9065ec4e8864adf432a80284e7ce28782a31f791e0842c252e445ca0
Transactions (1)
Coinbasefec7d62e9065ec…842c252e445ca0
1 in β†’ 1 out10.2600 XPM109 B
ALSo2SoE…vZXwVMRC
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.

7.019 Γ— 10⁹¹(92-digit number)
70198250465343744837…78676305753079709499
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
7.019 Γ— 10⁹¹(92-digit number)
70198250465343744837…78676305753079709499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.403 Γ— 10⁹²(93-digit number)
14039650093068748967…57352611506159418999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.807 Γ— 10⁹²(93-digit number)
28079300186137497935…14705223012318837999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.615 Γ— 10⁹²(93-digit number)
56158600372274995870…29410446024637675999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.123 Γ— 10⁹³(94-digit number)
11231720074454999174…58820892049275351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.246 Γ— 10⁹³(94-digit number)
22463440148909998348…17641784098550703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.492 Γ— 10⁹³(94-digit number)
44926880297819996696…35283568197101407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.985 Γ— 10⁹³(94-digit number)
89853760595639993392…70567136394202815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁴(95-digit number)
17970752119127998678…41134272788405631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.594 Γ— 10⁹⁴(95-digit number)
35941504238255997356…82268545576811263999
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:57,732,931 XPMΒ·at block #6,811,102 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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