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Block #1,371,296

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 8:37:36 AM Β· Difficulty 10.8133 Β· 5,454,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e69a19aad279ff7f8ac0998ad8081946c11745d70eb51a03215f43c3a9a36b61
View on Chainz β†—

Height

#1,371,296

Difficulty

10.813258

Transactions

2

Size

1.28 KB

Version

2

Bits

0ad031b5

Nonce

1,291,591,559

Timestamp

12/16/2015, 8:37:36 AM

Confirmations

5,454,101

Mined by

⛏️ P2SHAGe7pQ25PtYd5bbKCWrP7EVckM616p9UAE

Merkle Root

c7cfeadb1faf0852271fa2cba978f624db7d15d7d8fc0f8d976e30d66e5fccd3
Transactions (2)
Coinbase7403f35bc16f3f…3393aadd0c9da5
1 in β†’ 1 out8.5600 XPM109 B
AGe7pQ25…616p9UAE
6103b62716dfc9…2faf19c0b47064
7 in β†’ 2 out14.0096 XPM1.09 KB
APyMiHsT…aGoSFs5FALa8Fd3D…HQo53YYY
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.

5.080 Γ— 10⁹⁴(95-digit number)
50804759607614509530…37176262245960093919
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
5.080 Γ— 10⁹⁴(95-digit number)
50804759607614509530…37176262245960093919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁡(96-digit number)
10160951921522901906…74352524491920187839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.032 Γ— 10⁹⁡(96-digit number)
20321903843045803812…48705048983840375679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.064 Γ— 10⁹⁡(96-digit number)
40643807686091607624…97410097967680751359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.128 Γ— 10⁹⁡(96-digit number)
81287615372183215248…94820195935361502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.625 Γ— 10⁹⁢(97-digit number)
16257523074436643049…89640391870723005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.251 Γ— 10⁹⁢(97-digit number)
32515046148873286099…79280783741446010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.503 Γ— 10⁹⁢(97-digit number)
65030092297746572198…58561567482892021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.300 Γ— 10⁹⁷(98-digit number)
13006018459549314439…17123134965784043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.601 Γ— 10⁹⁷(98-digit number)
26012036919098628879…34246269931568087039
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:57,847,276 XPMΒ·at block #6,825,396 Β· updates every 60s
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