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Block #1,903,924

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/21/2016, 1:29:28 AM Β· Difficulty 10.7806 Β· 4,923,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2dbf88fbff0071839d67deeab287e5af60719161c5fbf2c01da4ba2734cbc232
View on Chainz β†—

Height

#1,903,924

Difficulty

10.780575

Transactions

1

Size

198 B

Version

2

Bits

0ac7d3c9

Nonce

37,659

Timestamp

12/21/2016, 1:29:28 AM

Confirmations

4,923,087

Mined by

⛏️ P2SHAcnbkVvgFTwALeZA7q2NM2e47Gpn4CFXJj

Merkle Root

27abdc842ed5377f7a07d4dc272fa9fa9093c82a175816cb12e4384b11fca641
Transactions (1)
Coinbase27abdc842ed537…e4384b11fca641
1 in β†’ 1 out8.5900 XPM109 B
AcnbkVvg…pn4CFXJj
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.

2.571 Γ— 10⁹³(94-digit number)
25714076670112306910…55962728822534578379
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
2.571 Γ— 10⁹³(94-digit number)
25714076670112306910…55962728822534578379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.142 Γ— 10⁹³(94-digit number)
51428153340224613820…11925457645069156759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁴(95-digit number)
10285630668044922764…23850915290138313519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁴(95-digit number)
20571261336089845528…47701830580276627039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.114 Γ— 10⁹⁴(95-digit number)
41142522672179691056…95403661160553254079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.228 Γ— 10⁹⁴(95-digit number)
82285045344359382113…90807322321106508159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁡(96-digit number)
16457009068871876422…81614644642213016319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.291 Γ— 10⁹⁡(96-digit number)
32914018137743752845…63229289284426032639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.582 Γ— 10⁹⁡(96-digit number)
65828036275487505690…26458578568852065279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.316 Γ— 10⁹⁢(97-digit number)
13165607255097501138…52917157137704130559
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:57,860,265 XPMΒ·at block #6,827,010 Β· updates every 60s
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