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Block #1,560,089

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/27/2016, 1:10:57 AM Β· Difficulty 10.7143 Β· 5,273,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3b2315eca31ca56aca064221dde8ab6a7a9a4efb72fb1627946385ca3282aab0
View on Chainz β†—

Height

#1,560,089

Difficulty

10.714310

Transactions

2

Size

835 B

Version

2

Bits

0ab6dd05

Nonce

617,483,320

Timestamp

4/27/2016, 1:10:57 AM

Confirmations

5,273,245

Mined by

⛏️ P2SHAH1NMHgbFqX6AYS9Azfc26VTLFVJC3KNLX

Merkle Root

4f5bbac79e03b883aa370eb154c89154d94790f81940078d582f481b02af83b5
Transactions (2)
Coinbasea265cee7be069f…3e34da07496d12
1 in β†’ 1 out8.7100 XPM109 B
AH1NMHgb…VJC3KNLX
d28fda64864ddb…6687b195bcd4b3
4 in β†’ 1 out1769.9900 XPM636 B
AHNccZy4…RwZSfQd3
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.

7.615 Γ— 10⁹⁴(95-digit number)
76159442432844846683…17215029882250872559
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
7.615 Γ— 10⁹⁴(95-digit number)
76159442432844846683…17215029882250872559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁡(96-digit number)
15231888486568969336…34430059764501745119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.046 Γ— 10⁹⁡(96-digit number)
30463776973137938673…68860119529003490239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.092 Γ— 10⁹⁡(96-digit number)
60927553946275877346…37720239058006980479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁢(97-digit number)
12185510789255175469…75440478116013960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.437 Γ— 10⁹⁢(97-digit number)
24371021578510350938…50880956232027921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.874 Γ— 10⁹⁢(97-digit number)
48742043157020701877…01761912464055843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.748 Γ— 10⁹⁢(97-digit number)
97484086314041403754…03523824928111687679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.949 Γ— 10⁹⁷(98-digit number)
19496817262808280750…07047649856223375359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.899 Γ— 10⁹⁷(98-digit number)
38993634525616561501…14095299712446750719
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:57,910,867 XPMΒ·at block #6,833,333 Β· updates every 60s
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