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Block #716,085

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/11/2014, 8:11:17 AM Β· Difficulty 10.9534 Β· 6,111,267 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bf52720d3f69dca9f57db3a9a77fb7af64d3cb87b7ef51aab9bfdab340a9ef64
View on Chainz β†—

Height

#716,085

Difficulty

10.953369

Transactions

1

Size

243 B

Version

2

Bits

0af40ffb

Nonce

1,348,011,762

Timestamp

9/11/2014, 8:11:17 AM

Confirmations

6,111,267

Mined by

⛏️ P2SHAJ2o6sWuGDC4FwKaNAha9eUK19BdumbXQh

Merkle Root

0670f1854f6c59d75c7393731a32f6f2e02da4b8eba83cc3680809ef6fa6c152
Transactions (1)
Coinbase0670f1854f6c59…0809ef6fa6c152
1 in β†’ 2 out8.3200 XPM152 B
AJ2o6sWu…BdumbXQhALPu3s2c…EJXLjVFh
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.

2.347 Γ— 10⁹⁷(98-digit number)
23474208886693715616…03682233404913919499
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
2.347 Γ— 10⁹⁷(98-digit number)
23474208886693715616…03682233404913919499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.694 Γ— 10⁹⁷(98-digit number)
46948417773387431233…07364466809827838999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.389 Γ— 10⁹⁷(98-digit number)
93896835546774862466…14728933619655677999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.877 Γ— 10⁹⁸(99-digit number)
18779367109354972493…29457867239311355999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.755 Γ— 10⁹⁸(99-digit number)
37558734218709944986…58915734478622711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.511 Γ— 10⁹⁸(99-digit number)
75117468437419889973…17831468957245423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.502 Γ— 10⁹⁹(100-digit number)
15023493687483977994…35662937914490847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.004 Γ— 10⁹⁹(100-digit number)
30046987374967955989…71325875828981695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.009 Γ— 10⁹⁹(100-digit number)
60093974749935911978…42651751657963391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.201 Γ— 10¹⁰⁰(101-digit number)
12018794949987182395…85303503315926783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.403 Γ— 10¹⁰⁰(101-digit number)
24037589899974364791…70607006631853567999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,862,915 XPMΒ·at block #6,827,351 Β· updates every 60s
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