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Block #2,134,552

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/27/2017, 8:47:52 AM Β· Difficulty 10.9079 Β· 4,699,237 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a14d3b05f007987a84594b093170f0f12246305e55154857c6158202ff105e0e
View on Chainz β†—

Height

#2,134,552

Difficulty

10.907853

Transactions

2

Size

1.83 KB

Version

2

Bits

0ae8690f

Nonce

1,277,297,394

Timestamp

5/27/2017, 8:47:52 AM

Confirmations

4,699,237

Mined by

⛏️ P2SHAX5ixRx8KcVmHUdWh6VVVjtWttV9DckzLm

Merkle Root

53ea541e7c15884dd9660a0220f76ef2fd91cff3916104a4eb60b319c51f1d21
Transactions (2)
Coinbase8d025170d3a024…50f55dadf05a35
1 in β†’ 1 out8.4300 XPM109 B
AX5ixRx8…V9DckzLm
78f7a9a5807497…df9b66c1256a80
11 in β†’ 1 out2729.4675 XPM1.63 KB
AbfHPQRP…cc1QCTYa
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.

7.697 Γ— 10⁹³(94-digit number)
76973934118432636062…40384712952028148499
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
7.697 Γ— 10⁹³(94-digit number)
76973934118432636062…40384712952028148499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.539 Γ— 10⁹⁴(95-digit number)
15394786823686527212…80769425904056296999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.078 Γ— 10⁹⁴(95-digit number)
30789573647373054425…61538851808112593999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.157 Γ— 10⁹⁴(95-digit number)
61579147294746108850…23077703616225187999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁡(96-digit number)
12315829458949221770…46155407232450375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.463 Γ— 10⁹⁡(96-digit number)
24631658917898443540…92310814464900751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.926 Γ— 10⁹⁡(96-digit number)
49263317835796887080…84621628929801503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.852 Γ— 10⁹⁡(96-digit number)
98526635671593774160…69243257859603007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.970 Γ— 10⁹⁢(97-digit number)
19705327134318754832…38486515719206015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.941 Γ— 10⁹⁢(97-digit number)
39410654268637509664…76973031438412031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.882 Γ— 10⁹⁢(97-digit number)
78821308537275019328…53946062876824063999
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:57,914,532 XPMΒ·at block #6,833,788 Β· updates every 60s
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