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Block #910,310

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/26/2015, 5:16:38 AM Β· Difficulty 10.9332 Β· 5,896,561 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58dfa82707d9d144a89b395da5d227ef4815b588285032bdd33cc54a1e84901d
View on Chainz β†—

Height

#910,310

Difficulty

10.933248

Transactions

2

Size

1.14 KB

Version

2

Bits

0aeee950

Nonce

168,212,620

Timestamp

1/26/2015, 5:16:38 AM

Confirmations

5,896,561

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a7440a36fb04d55af09ad470a1989c72ba9b0bbdb6cc4ac4e6986d9c59f10656
Transactions (2)
Coinbase474c0875557997…3ad0fe65f45a60
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
9708333274b7ee…09baab35060dcc
6 in β†’ 2 out358.6336 XPM965 B
AXDtVm9J…U6mC5pKcAUSxVrre…B27XD3yv
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.

4.033 Γ— 10⁹⁢(97-digit number)
40339113187267367042…71645959505720255039
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
4.033 Γ— 10⁹⁢(97-digit number)
40339113187267367042…71645959505720255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.067 Γ— 10⁹⁢(97-digit number)
80678226374534734085…43291919011440510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.613 Γ— 10⁹⁷(98-digit number)
16135645274906946817…86583838022881020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.227 Γ— 10⁹⁷(98-digit number)
32271290549813893634…73167676045762040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.454 Γ— 10⁹⁷(98-digit number)
64542581099627787268…46335352091524080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.290 Γ— 10⁹⁸(99-digit number)
12908516219925557453…92670704183048161279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.581 Γ— 10⁹⁸(99-digit number)
25817032439851114907…85341408366096322559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.163 Γ— 10⁹⁸(99-digit number)
51634064879702229814…70682816732192645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁹(100-digit number)
10326812975940445962…41365633464385290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.065 Γ— 10⁹⁹(100-digit number)
20653625951880891925…82731266928770580479
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:57,699,075 XPMΒ·at block #6,806,870 Β· updates every 60s
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