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Block #830,714

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2014, 4:13:33 PM Β· Difficulty 10.9789 Β· 6,012,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69f529f122960168c3e5f814ed7e7aac325814d930cad4467127de1c5b52da27
View on Chainz β†—

Height

#830,714

Difficulty

10.978862

Transactions

2

Size

9.82 KB

Version

2

Bits

0afa96b5

Nonce

295,129,355

Timestamp

11/27/2014, 4:13:33 PM

Confirmations

6,012,458

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b79c81cc238eb75bb18fa2411c6e9ace7a20c0874c5f2460d26a7cf64b383861
Transactions (2)
Coinbased01fd3f8f5f6aa…637aa3b01099db
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
e6083b74c512f2…3b64481e58cb14
66 in β†’ 2 out500.0101 XPM9.62 KB
AZPdQNcX…kdS6tQhEAJjnK9uC…VreFquR4
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.

3.037 Γ— 10⁹⁡(96-digit number)
30376902363528098691…00976997119038206299
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
3.037 Γ— 10⁹⁡(96-digit number)
30376902363528098691…00976997119038206299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.075 Γ— 10⁹⁡(96-digit number)
60753804727056197383…01953994238076412599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁢(97-digit number)
12150760945411239476…03907988476152825199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁢(97-digit number)
24301521890822478953…07815976952305650399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁢(97-digit number)
48603043781644957906…15631953904611300799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.720 Γ— 10⁹⁢(97-digit number)
97206087563289915813…31263907809222601599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁷(98-digit number)
19441217512657983162…62527815618445203199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁷(98-digit number)
38882435025315966325…25055631236890406399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.776 Γ— 10⁹⁷(98-digit number)
77764870050631932651…50111262473780812799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁸(99-digit number)
15552974010126386530…00222524947561625599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.110 Γ— 10⁹⁸(99-digit number)
31105948020252773060…00445049895123251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
6.221 Γ— 10⁹⁸(99-digit number)
62211896040505546120…00890099790246502399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,989,742 XPMΒ·at block #6,843,171 Β· updates every 60s
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