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Block #149,097

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 3:43:07 AM Β· Difficulty 9.8567 Β· 6,661,126 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bb925c787d7f556dbad5d5f3bfe762298b60af9442c6c7b2170b22c26c931662
View on Chainz β†—

Height

#149,097

Difficulty

9.856730

Transactions

1

Size

198 B

Version

2

Bits

09db52af

Nonce

3,835

Timestamp

9/4/2013, 3:43:07 AM

Confirmations

6,661,126

Mined by

⛏️ P2SHAGLpT5zBCy42ej8dmuMEVvxHoCBnHeFXQg

Merkle Root

d173514985ff4f6c46e67fcd8af9f46c206250749bf987939a2596b9c15f90ed
Transactions (1)
Coinbased173514985ff4f…2596b9c15f90ed
1 in β†’ 1 out10.2800 XPM109 B
AGLpT5zB…BnHeFXQg
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.

4.740 Γ— 10⁹²(93-digit number)
47400405654134298554…89522724865340195999
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
4.740 Γ— 10⁹²(93-digit number)
47400405654134298554…89522724865340195999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.480 Γ— 10⁹²(93-digit number)
94800811308268597108…79045449730680391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.896 Γ— 10⁹³(94-digit number)
18960162261653719421…58090899461360783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.792 Γ— 10⁹³(94-digit number)
37920324523307438843…16181798922721567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.584 Γ— 10⁹³(94-digit number)
75840649046614877686…32363597845443135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.516 Γ— 10⁹⁴(95-digit number)
15168129809322975537…64727195690886271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.033 Γ— 10⁹⁴(95-digit number)
30336259618645951074…29454391381772543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.067 Γ— 10⁹⁴(95-digit number)
60672519237291902149…58908782763545087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁡(96-digit number)
12134503847458380429…17817565527090175999
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:57,725,860 XPMΒ·at block #6,810,222 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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