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Block #671,286

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/10/2014, 4:44:03 AM Β· Difficulty 10.9640 Β· 6,130,124 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
440f79df810cedd9adc36f173643b50398a100c87719dc068425c710be285eaf
View on Chainz β†—

Height

#671,286

Difficulty

10.964042

Transactions

3

Size

657 B

Version

2

Bits

0af6cb76

Nonce

27,721,146

Timestamp

8/10/2014, 4:44:03 AM

Confirmations

6,130,124

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c84ffb7669454c7ef8e1032b93c19e1c551b62ef17219d9497fd60f9bd9e0432
Transactions (3)
Coinbase7d355555108ed8…c431741c5c6703
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
d4756007102f13…95deea83a1ebc7
1 in β†’ 2 out7.2870 XPM226 B
ARpjHv1k…4F9NvuWNAZVXgCpe…8jxR5a8x
5af697c61f065b…40a6f54cd9670e
1 in β†’ 2 out2.1934 XPM225 B
AWbYt63i…H2mAW2WzAafqHBxL…ooM7pKWf
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.

1.360 Γ— 10⁹⁡(96-digit number)
13609074832965761399…45363512889869488639
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
1.360 Γ— 10⁹⁡(96-digit number)
13609074832965761399…45363512889869488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.721 Γ— 10⁹⁡(96-digit number)
27218149665931522798…90727025779738977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.443 Γ— 10⁹⁡(96-digit number)
54436299331863045596…81454051559477954559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁢(97-digit number)
10887259866372609119…62908103118955909119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.177 Γ— 10⁹⁢(97-digit number)
21774519732745218238…25816206237911818239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.354 Γ— 10⁹⁢(97-digit number)
43549039465490436476…51632412475823636479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.709 Γ— 10⁹⁢(97-digit number)
87098078930980872953…03264824951647272959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁷(98-digit number)
17419615786196174590…06529649903294545919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.483 Γ— 10⁹⁷(98-digit number)
34839231572392349181…13059299806589091839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.967 Γ— 10⁹⁷(98-digit number)
69678463144784698363…26118599613178183679
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:57,655,350 XPMΒ·at block #6,801,409 Β· updates every 60s
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