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Block #97,506

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2013, 6:21:42 PM Β· Difficulty 9.3083 Β· 6,705,285 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b99db4adaa40632c13cbc2da7dce7cf7e319fa809e666d41ed1c1f93855a6a5c
View on Chainz β†—

Height

#97,506

Difficulty

9.308290

Transactions

1

Size

200 B

Version

2

Bits

094eec1f

Nonce

1,171,712

Timestamp

8/4/2013, 6:21:42 PM

Confirmations

6,705,285

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

521aeb0ea833b621dbf1275c3b737a210e78e818eb33f8ae2223939a6bd15f9f
Transactions (1)
Coinbase521aeb0ea833b6…23939a6bd15f9f
1 in β†’ 1 out11.5200 XPM109 B
AezMwyLP…rTg7Eyfk
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.

2.520 Γ— 10⁹⁢(97-digit number)
25202157733938340597…49604634270847482149
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
2.520 Γ— 10⁹⁢(97-digit number)
25202157733938340597…49604634270847482149
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.040 Γ— 10⁹⁢(97-digit number)
50404315467876681195…99209268541694964299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁷(98-digit number)
10080863093575336239…98418537083389928599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁷(98-digit number)
20161726187150672478…96837074166779857199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.032 Γ— 10⁹⁷(98-digit number)
40323452374301344956…93674148333559714399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.064 Γ— 10⁹⁷(98-digit number)
80646904748602689913…87348296667119428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁸(99-digit number)
16129380949720537982…74696593334238857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.225 Γ— 10⁹⁸(99-digit number)
32258761899441075965…49393186668477715199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.451 Γ— 10⁹⁸(99-digit number)
64517523798882151930…98786373336955430399
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:57,666,354 XPMΒ·at block #6,802,790 Β· updates every 60s
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