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Block #912,778

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/28/2015, 4:36:35 AM Β· Difficulty 10.9281 Β· 5,882,277 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35e206d7c82a922ee44c1b54d660d48cea3b11a69b76bad16af5b300c99d97c5
View on Chainz β†—

Height

#912,778

Difficulty

10.928142

Transactions

2

Size

2.30 KB

Version

2

Bits

0aed9aba

Nonce

69,286,643

Timestamp

1/28/2015, 4:36:35 AM

Confirmations

5,882,277

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e27144a07db22233f835f2e71a17251f17e3e1abfcaa3f4b088121177b6f3115
Transactions (2)
Coinbaseb362e5c1df9c87…17313326143339
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
42e840c86682b3…c780c12fcb58ef
14 in β†’ 2 out1807.9212 XPM2.10 KB
AcAFW717…V1pWEX3JALRUm8vb…f8RHay8i
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.

5.690 Γ— 10⁹⁡(96-digit number)
56905771426055957079…59647295833556251439
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
5.690 Γ— 10⁹⁡(96-digit number)
56905771426055957079…59647295833556251439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁢(97-digit number)
11381154285211191415…19294591667112502879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.276 Γ— 10⁹⁢(97-digit number)
22762308570422382831…38589183334225005759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.552 Γ— 10⁹⁢(97-digit number)
45524617140844765663…77178366668450011519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.104 Γ— 10⁹⁢(97-digit number)
91049234281689531327…54356733336900023039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.820 Γ— 10⁹⁷(98-digit number)
18209846856337906265…08713466673800046079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.641 Γ— 10⁹⁷(98-digit number)
36419693712675812531…17426933347600092159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.283 Γ— 10⁹⁷(98-digit number)
72839387425351625062…34853866695200184319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.456 Γ— 10⁹⁸(99-digit number)
14567877485070325012…69707733390400368639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.913 Γ— 10⁹⁸(99-digit number)
29135754970140650024…39415466780800737279
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:57,604,481 XPMΒ·at block #6,795,054 Β· updates every 60s
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