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Block #780,020

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/23/2014, 12:12:26 PM Β· Difficulty 10.9772 Β· 6,033,831 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f967b23e861948f892cdbb4fde741c5a412b5572340ecf9436dbd5dd8e81e6d6
View on Chainz β†—

Height

#780,020

Difficulty

10.977161

Transactions

1

Size

242 B

Version

2

Bits

0afa273e

Nonce

1,346,746,593

Timestamp

10/23/2014, 12:12:26 PM

Confirmations

6,033,831

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

e2818be635713c4cd15475b919b024cb52f109892c9658aa66f981c0746479d6
Transactions (1)
Coinbasee2818be635713c…f981c0746479d6
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…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.

6.784 Γ— 10⁹⁴(95-digit number)
67845067638474149807…89155134265570828439
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
6.784 Γ— 10⁹⁴(95-digit number)
67845067638474149807…89155134265570828439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.356 Γ— 10⁹⁡(96-digit number)
13569013527694829961…78310268531141656879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.713 Γ— 10⁹⁡(96-digit number)
27138027055389659922…56620537062283313759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.427 Γ— 10⁹⁡(96-digit number)
54276054110779319845…13241074124566627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.085 Γ— 10⁹⁢(97-digit number)
10855210822155863969…26482148249133255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.171 Γ— 10⁹⁢(97-digit number)
21710421644311727938…52964296498266510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.342 Γ— 10⁹⁢(97-digit number)
43420843288623455876…05928592996533020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.684 Γ— 10⁹⁢(97-digit number)
86841686577246911752…11857185993066040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.736 Γ— 10⁹⁷(98-digit number)
17368337315449382350…23714371986132080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.473 Γ— 10⁹⁷(98-digit number)
34736674630898764701…47428743972264161279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.947 Γ— 10⁹⁷(98-digit number)
69473349261797529402…94857487944528322559
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:57,754,870 XPMΒ·at block #6,813,849 Β· updates every 60s
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