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Block #108,262

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2013, 10:43:44 PM Β· Difficulty 9.6446 Β· 6,695,023 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
994ceaa16afb48fc1575c6cf3e926239c5d655e23847a3e8c5cdf1c2c452f3d7
View on Chainz β†—

Height

#108,262

Difficulty

9.644633

Transactions

1

Size

201 B

Version

2

Bits

09a506a5

Nonce

134,521

Timestamp

8/9/2013, 10:43:44 PM

Confirmations

6,695,023

Mined by

⛏️ P2SHAJwT4t7mqNZ7nwyuBKJTxL3n2nrXZrFS9k

Merkle Root

511ca4b152b1a412859968ec034a171b20f62dc30b017417f2eb820fb64b95b6
Transactions (1)
Coinbase511ca4b152b1a4…eb820fb64b95b6
1 in β†’ 1 out10.7300 XPM109 B
AJwT4t7m…rXZrFS9k
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.

1.696 Γ— 10⁹⁸(99-digit number)
16968719422857038573…35614727463653327449
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
1.696 Γ— 10⁹⁸(99-digit number)
16968719422857038573…35614727463653327449
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.393 Γ— 10⁹⁸(99-digit number)
33937438845714077146…71229454927306654899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.787 Γ— 10⁹⁸(99-digit number)
67874877691428154292…42458909854613309799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.357 Γ— 10⁹⁹(100-digit number)
13574975538285630858…84917819709226619599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.714 Γ— 10⁹⁹(100-digit number)
27149951076571261716…69835639418453239199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.429 Γ— 10⁹⁹(100-digit number)
54299902153142523433…39671278836906478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.085 Γ— 10¹⁰⁰(101-digit number)
10859980430628504686…79342557673812956799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.171 Γ— 10¹⁰⁰(101-digit number)
21719960861257009373…58685115347625913599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.343 Γ— 10¹⁰⁰(101-digit number)
43439921722514018747…17370230695251827199
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:57,670,305 XPMΒ·at block #6,803,284 Β· updates every 60s
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