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Block #764,863

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/12/2014, 9:13:42 PM Β· Difficulty 10.9773 Β· 6,045,377 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f27fb4d14d12c6f4c82ada085ff7f422d58564b95bf61062e4db8e57a330d034
View on Chainz β†—

Height

#764,863

Difficulty

10.977271

Transactions

2

Size

2.88 KB

Version

2

Bits

0afa2e73

Nonce

123,010,960

Timestamp

10/12/2014, 9:13:42 PM

Confirmations

6,045,377

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

38b6039ecd9dbe9b4b0fb43919bea49016dcac81e34e73a0ce23d42097dd7d1a
Transactions (2)
Coinbase4032b457eb4caa…3fa654154002e0
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
7dc675e3b8427a…faac084800cef9
18 in β†’ 2 out126.5235 XPM2.68 KB
APjCEgmQ…5dwBRTvpAWPWaw6y…7a24WEid
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.

2.408 Γ— 10⁹⁷(98-digit number)
24087181049723210990…47019593879080005119
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
2.408 Γ— 10⁹⁷(98-digit number)
24087181049723210990…47019593879080005119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.817 Γ— 10⁹⁷(98-digit number)
48174362099446421980…94039187758160010239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.634 Γ— 10⁹⁷(98-digit number)
96348724198892843961…88078375516320020479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.926 Γ— 10⁹⁸(99-digit number)
19269744839778568792…76156751032640040959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.853 Γ— 10⁹⁸(99-digit number)
38539489679557137584…52313502065280081919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.707 Γ— 10⁹⁸(99-digit number)
77078979359114275169…04627004130560163839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.541 Γ— 10⁹⁹(100-digit number)
15415795871822855033…09254008261120327679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.083 Γ— 10⁹⁹(100-digit number)
30831591743645710067…18508016522240655359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.166 Γ— 10⁹⁹(100-digit number)
61663183487291420135…37016033044481310719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.233 Γ— 10¹⁰⁰(101-digit number)
12332636697458284027…74032066088962621439
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:57,725,998 XPMΒ·at block #6,810,239 Β· updates every 60s
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