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Block #277,911

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2013, 6:36:06 PM Β· Difficulty 9.9676 Β· 6,531,537 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
543e36534dad82cbec2fbff70bbf7e83d830b3627ea42233766754af2a93c0ee
View on Chainz β†—

Height

#277,911

Difficulty

9.967558

Transactions

1

Size

204 B

Version

2

Bits

09f7b1e2

Nonce

532,485

Timestamp

11/27/2013, 6:36:06 PM

Confirmations

6,531,537

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

928a933234dc195d6f8b5a59d0c9142a65944fbb7175e0897db262be236fb9a9
Transactions (1)
Coinbase928a933234dc19…b262be236fb9a9
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.

1.275 Γ— 10⁹¹(92-digit number)
12754620672751483378…01116207430239937599
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
1.275 Γ— 10⁹¹(92-digit number)
12754620672751483378…01116207430239937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.550 Γ— 10⁹¹(92-digit number)
25509241345502966756…02232414860479875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.101 Γ— 10⁹¹(92-digit number)
51018482691005933513…04464829720959750399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.020 Γ— 10⁹²(93-digit number)
10203696538201186702…08929659441919500799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.040 Γ— 10⁹²(93-digit number)
20407393076402373405…17859318883839001599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.081 Γ— 10⁹²(93-digit number)
40814786152804746810…35718637767678003199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.162 Γ— 10⁹²(93-digit number)
81629572305609493621…71437275535356006399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.632 Γ— 10⁹³(94-digit number)
16325914461121898724…42874551070712012799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.265 Γ— 10⁹³(94-digit number)
32651828922243797448…85749102141424025599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,719,655 XPMΒ·at block #6,809,447 Β· updates every 60s
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