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Block #102,992

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 9:20:04 AM Β· Difficulty 9.5126 Β· 6,712,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8107c6b8ffe3dc2a23f4e4fe2084c497d2aae3b7dd513e0987da5c9a56540e59
View on Chainz β†—

Height

#102,992

Difficulty

9.512581

Transactions

1

Size

200 B

Version

2

Bits

09833884

Nonce

166,082

Timestamp

8/7/2013, 9:20:04 AM

Confirmations

6,712,854

Mined by

⛏️ P2SHAdrHMrr5enNPbRc3neFNXyrxuNTacb8YKK

Merkle Root

88d765342c994cef6c4c3e35a725264ce36c1979f23b093e054539ece7dd1aa3
Transactions (1)
Coinbase88d765342c994c…4539ece7dd1aa3
1 in β†’ 1 out11.0300 XPM109 B
AdrHMrr5…Tacb8YKK
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.

1.063 Γ— 10⁹⁸(99-digit number)
10638549620351037951…85303587135466038239
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
1.063 Γ— 10⁹⁸(99-digit number)
10638549620351037951…85303587135466038239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁸(99-digit number)
21277099240702075903…70607174270932076479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.255 Γ— 10⁹⁸(99-digit number)
42554198481404151807…41214348541864152959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.510 Γ— 10⁹⁸(99-digit number)
85108396962808303615…82428697083728305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.702 Γ— 10⁹⁹(100-digit number)
17021679392561660723…64857394167456611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.404 Γ— 10⁹⁹(100-digit number)
34043358785123321446…29714788334913223679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.808 Γ— 10⁹⁹(100-digit number)
68086717570246642892…59429576669826447359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.361 Γ— 10¹⁰⁰(101-digit number)
13617343514049328578…18859153339652894719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.723 Γ— 10¹⁰⁰(101-digit number)
27234687028098657156…37718306679305789439
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:57,770,878 XPMΒ·at block #6,815,845 Β· updates every 60s
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