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Block #1,332,311

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/18/2015, 5:53:12 PM Β· Difficulty 10.8385 Β· 5,484,633 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97082788e763dc25d93f10ea4b7b0c6f88ca7c2094f54ebab9e648f00e4667a5
View on Chainz β†—

Height

#1,332,311

Difficulty

10.838466

Transactions

2

Size

21.22 KB

Version

2

Bits

0ad6a5ba

Nonce

1,343,781,367

Timestamp

11/18/2015, 5:53:12 PM

Confirmations

5,484,633

Mined by

⛏️ P2SHAbXqpYMcQ1e5kBfmNJAe48ZKux8ucbhRVg

Merkle Root

82e584fe9c8aba901e590cf364067c30019081799b6f5de824f0bd8c891c3802
Transactions (2)
Coinbase0b0c0281f12cd9…a5a7ca739d9053
1 in β†’ 1 out8.7400 XPM109 B
AbXqpYMc…8ucbhRVg
f133fc804b439b…bf986d341c4387
145 in β†’ 2 out995.0000 XPM21.03 KB
AdzHczk8…7QABT6UPARGwXWk4…oSKV612d
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.

1.907 Γ— 10⁹⁡(96-digit number)
19074949150342257374…59081171054482485759
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
1.907 Γ— 10⁹⁡(96-digit number)
19074949150342257374…59081171054482485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.814 Γ— 10⁹⁡(96-digit number)
38149898300684514749…18162342108964971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.629 Γ— 10⁹⁡(96-digit number)
76299796601369029499…36324684217929943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.525 Γ— 10⁹⁢(97-digit number)
15259959320273805899…72649368435859886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.051 Γ— 10⁹⁢(97-digit number)
30519918640547611799…45298736871719772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.103 Γ— 10⁹⁢(97-digit number)
61039837281095223599…90597473743439544319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁷(98-digit number)
12207967456219044719…81194947486879088639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.441 Γ— 10⁹⁷(98-digit number)
24415934912438089439…62389894973758177279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.883 Γ— 10⁹⁷(98-digit number)
48831869824876178879…24779789947516354559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.766 Γ— 10⁹⁷(98-digit number)
97663739649752357758…49559579895032709119
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:57,779,595 XPMΒ·at block #6,816,943 Β· updates every 60s
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