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Block #277,713

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2013, 4:34:19 PM Β· Difficulty 9.9671 Β· 6,561,862 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89730e43780a5a0859ae417df81cf7d4fd2eff3b01a991633ee0fb2c6ab84196
View on Chainz β†—

Height

#277,713

Difficulty

9.967052

Transactions

1

Size

207 B

Version

2

Bits

09f790b5

Nonce

67,110,199

Timestamp

11/27/2013, 4:34:19 PM

Confirmations

6,561,862

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

2225ca393ef75837483eb223e84855fc115350fe8cc874aaf4bfced64efedd0b
Transactions (1)
Coinbase2225ca393ef758…bfced64efedd0b
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.738 Γ— 10⁹⁢(97-digit number)
47381201508689034093…31223841243938990079
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
4.738 Γ— 10⁹⁢(97-digit number)
47381201508689034093…31223841243938990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.476 Γ— 10⁹⁢(97-digit number)
94762403017378068187…62447682487877980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.895 Γ— 10⁹⁷(98-digit number)
18952480603475613637…24895364975755960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.790 Γ— 10⁹⁷(98-digit number)
37904961206951227274…49790729951511920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.580 Γ— 10⁹⁷(98-digit number)
75809922413902454549…99581459903023841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.516 Γ— 10⁹⁸(99-digit number)
15161984482780490909…99162919806047682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.032 Γ— 10⁹⁸(99-digit number)
30323968965560981819…98325839612095365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.064 Γ— 10⁹⁸(99-digit number)
60647937931121963639…96651679224190730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁹(100-digit number)
12129587586224392727…93303358448381460479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁹(100-digit number)
24259175172448785455…86606716896762920959
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:57,960,886 XPMΒ·at block #6,839,574 Β· updates every 60s
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