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Block #1,260,985

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/30/2015, 12:14:25 PM Β· Difficulty 10.8214 Β· 5,543,085 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
940dc987dc65ab54ea1e0dd30540377dfcdb5cb57f35255c1bcdbf463760a835
View on Chainz β†—

Height

#1,260,985

Difficulty

10.821447

Transactions

1

Size

200 B

Version

2

Bits

0ad24a60

Nonce

1,355,501,664

Timestamp

9/30/2015, 12:14:25 PM

Confirmations

5,543,085

Mined by

⛏️ P2SHAH8A9fZk564rzrTsg1Q5JEeZUGhPnerFJQ

Merkle Root

71c4c6278b33109b3e9c1ede5deb7c2726bf431f2af57d2188c60e1367dea217
Transactions (1)
Coinbase71c4c6278b3310…c60e1367dea217
1 in β†’ 1 out8.5300 XPM110 B
AH8A9fZk…hPnerFJQ
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.

1.720 Γ— 10⁹⁡(96-digit number)
17208996860893475540…91628400474404735919
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
1.720 Γ— 10⁹⁡(96-digit number)
17208996860893475540…91628400474404735919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.441 Γ— 10⁹⁡(96-digit number)
34417993721786951080…83256800948809471839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.883 Γ— 10⁹⁡(96-digit number)
68835987443573902161…66513601897618943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁢(97-digit number)
13767197488714780432…33027203795237887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.753 Γ— 10⁹⁢(97-digit number)
27534394977429560864…66054407590475774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.506 Γ— 10⁹⁢(97-digit number)
55068789954859121729…32108815180951549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.101 Γ— 10⁹⁷(98-digit number)
11013757990971824345…64217630361903098879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.202 Γ— 10⁹⁷(98-digit number)
22027515981943648691…28435260723806197759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.405 Γ— 10⁹⁷(98-digit number)
44055031963887297383…56870521447612395519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.811 Γ— 10⁹⁷(98-digit number)
88110063927774594766…13741042895224791039
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:57,676,616 XPMΒ·at block #6,804,069 Β· updates every 60s
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