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Block #1,191,991

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2015, 4:19:48 PM Β· Difficulty 10.8612 Β· 5,618,230 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8f29ef5c32da4626f732e4bc7c271db0034a96b2057853c0627312afce21c0f9
View on Chainz β†—

Height

#1,191,991

Difficulty

10.861233

Transactions

2

Size

427 B

Version

2

Bits

0adc79c0

Nonce

738,710,344

Timestamp

8/12/2015, 4:19:48 PM

Confirmations

5,618,230

Mined by

⛏️ P2SHAWRTUF9LG4WFBhm51twK2hFM7Pm1t8WEGN

Merkle Root

b248836f739a76c470db8349cc2fac07680727dd44210967126dfd0d5f07f0ad
Transactions (2)
Coinbasecf53b9f8897292…7814d5b46fce5f
1 in β†’ 1 out8.4700 XPM110 B
AWRTUF9L…m1t8WEGN
db3972d6e6faf1…4c949323ca1d46
1 in β†’ 2 out2.1039 XPM226 B
AKgZq14B…yTzTaYCFAH9HenSr…7F72AXru
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.

1.627 Γ— 10⁹⁢(97-digit number)
16273441115772084067…05175747249318374399
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
1.627 Γ— 10⁹⁢(97-digit number)
16273441115772084067…05175747249318374399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.254 Γ— 10⁹⁢(97-digit number)
32546882231544168135…10351494498636748799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.509 Γ— 10⁹⁢(97-digit number)
65093764463088336270…20702988997273497599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.301 Γ— 10⁹⁷(98-digit number)
13018752892617667254…41405977994546995199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.603 Γ— 10⁹⁷(98-digit number)
26037505785235334508…82811955989093990399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.207 Γ— 10⁹⁷(98-digit number)
52075011570470669016…65623911978187980799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁸(99-digit number)
10415002314094133803…31247823956375961599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.083 Γ— 10⁹⁸(99-digit number)
20830004628188267606…62495647912751923199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.166 Γ— 10⁹⁸(99-digit number)
41660009256376535213…24991295825503846399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.332 Γ— 10⁹⁸(99-digit number)
83320018512753070426…49982591651007692799
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:57,725,843 XPMΒ·at block #6,810,220 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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