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Block #888,777

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2015, 7:15:55 PM Β· Difficulty 10.9555 Β· 5,919,109 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd0f27e435c07a135c8b94574cd8941a938d1a9cb0febe0470fe9a7ddbaba1c1
View on Chainz β†—

Height

#888,777

Difficulty

10.955513

Transactions

2

Size

547 B

Version

2

Bits

0af49c80

Nonce

905,302,159

Timestamp

1/9/2015, 7:15:55 PM

Confirmations

5,919,109

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dfc687a5e82775a8ecf27bbc8754d8e718f31e323cb7043d7a49ebfbbe103d3e
Transactions (2)
Coinbasea28b996d0f153f…6725097d6740d7
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
12036efa2e917f…ffa01bd1083509
2 in β†’ 1 out12.9900 XPM340 B
ALG61FV8…ZKkt4mg7
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.

9.290 Γ— 10⁹⁷(98-digit number)
92902017110990017689…84211224734129582079
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
9.290 Γ— 10⁹⁷(98-digit number)
92902017110990017689…84211224734129582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁸(99-digit number)
18580403422198003537…68422449468259164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁸(99-digit number)
37160806844396007075…36844898936518328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.432 Γ— 10⁹⁸(99-digit number)
74321613688792014151…73689797873036656639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.486 Γ— 10⁹⁹(100-digit number)
14864322737758402830…47379595746073313279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.972 Γ— 10⁹⁹(100-digit number)
29728645475516805660…94759191492146626559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.945 Γ— 10⁹⁹(100-digit number)
59457290951033611321…89518382984293253119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.189 Γ— 10¹⁰⁰(101-digit number)
11891458190206722264…79036765968586506239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.378 Γ— 10¹⁰⁰(101-digit number)
23782916380413444528…58073531937173012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.756 Γ— 10¹⁰⁰(101-digit number)
47565832760826889057…16147063874346024959
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:57,707,123 XPMΒ·at block #6,807,885 Β· updates every 60s
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