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Block #704,398

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2014, 5:35:23 PM Β· Difficulty 10.9591 Β· 6,126,334 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38a3f4124e0eb8af2e1074c0ed050d1bf1a82f8de47e7cd653fcf8812b624c95
View on Chainz β†—

Height

#704,398

Difficulty

10.959135

Transactions

2

Size

1.43 KB

Version

2

Bits

0af589de

Nonce

4,211,123,929

Timestamp

9/2/2014, 5:35:23 PM

Confirmations

6,126,334

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f0cc671f35072a4288fccc970794a09c139c9a01393139c20b9af905063f9c37
Transactions (2)
Coinbase95a04f6617d19b…b71d0fe268fc71
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
7229735aad98d1…460588211f2272
8 in β†’ 2 out1222.0209 XPM1.23 KB
ANgxifUJ…W8Mg8pXkAKRxN6Ku…Bht1Dc4r
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.

1.083 Γ— 10⁹⁴(95-digit number)
10836694623645679613…23375255047214143919
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
1.083 Γ— 10⁹⁴(95-digit number)
10836694623645679613…23375255047214143919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.167 Γ— 10⁹⁴(95-digit number)
21673389247291359227…46750510094428287839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.334 Γ— 10⁹⁴(95-digit number)
43346778494582718454…93501020188856575679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.669 Γ— 10⁹⁴(95-digit number)
86693556989165436909…87002040377713151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.733 Γ— 10⁹⁡(96-digit number)
17338711397833087381…74004080755426302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.467 Γ— 10⁹⁡(96-digit number)
34677422795666174763…48008161510852605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.935 Γ— 10⁹⁡(96-digit number)
69354845591332349527…96016323021705210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁢(97-digit number)
13870969118266469905…92032646043410421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.774 Γ— 10⁹⁢(97-digit number)
27741938236532939810…84065292086820843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.548 Γ— 10⁹⁢(97-digit number)
55483876473065879621…68130584173641687039
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:57,889,992 XPMΒ·at block #6,830,731 Β· updates every 60s
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