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Block #70,861

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 3:51:46 PM Β· Difficulty 8.9926 Β· 6,732,763 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7dc35d78145f58f24def1accbd060760ad025039a96b267300d5b2a53c74a810
View on Chainz β†—

Height

#70,861

Difficulty

8.992598

Transactions

1

Size

198 B

Version

2

Bits

08fe1aec

Nonce

105

Timestamp

7/20/2013, 3:51:46 PM

Confirmations

6,732,763

Mined by

⛏️ P2SHAawzRYLpHU7wZxoYUFawXzGZd4NJSmHiTJ

Merkle Root

accc9ac1664b21d6c86600aeb723fde09f3ebf1480940e4c6bcb80a9b3a51f44
Transactions (1)
Coinbaseaccc9ac1664b21…cb80a9b3a51f44
1 in β†’ 1 out12.3500 XPM110 B
AawzRYLp…NJSmHiTJ
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.

1.786 Γ— 10⁹⁰(91-digit number)
17867978552331486395…79477696216732610659
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
1.786 Γ— 10⁹⁰(91-digit number)
17867978552331486395…79477696216732610659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁰(91-digit number)
35735957104662972791…58955392433465221319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.147 Γ— 10⁹⁰(91-digit number)
71471914209325945583…17910784866930442639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.429 Γ— 10⁹¹(92-digit number)
14294382841865189116…35821569733860885279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.858 Γ— 10⁹¹(92-digit number)
28588765683730378233…71643139467721770559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.717 Γ— 10⁹¹(92-digit number)
57177531367460756466…43286278935443541119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.143 Γ— 10⁹²(93-digit number)
11435506273492151293…86572557870887082239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.287 Γ— 10⁹²(93-digit number)
22871012546984302586…73145115741774164479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.574 Γ— 10⁹²(93-digit number)
45742025093968605173…46290231483548328959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.148 Γ— 10⁹²(93-digit number)
91484050187937210346…92580462967096657919
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:57,673,023 XPMΒ·at block #6,803,623 Β· updates every 60s
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