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Block #1,076,896

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2015, 1:45:36 PM Β· Difficulty 10.7566 Β· 5,726,748 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ad766149ce7d894f5d127c6545085775b96416dacb7153af1fb9bb06ffad3d1
View on Chainz β†—

Height

#1,076,896

Difficulty

10.756561

Transactions

1

Size

201 B

Version

2

Bits

0ac1adfb

Nonce

98,812,444

Timestamp

5/26/2015, 1:45:36 PM

Confirmations

5,726,748

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

da5e961cee754590f03de58a81c8c9640652a71323706bf14c80bf8223ff37af
Transactions (1)
Coinbaseda5e961cee7545…80bf8223ff37af
1 in β†’ 1 out8.6300 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

5.765 Γ— 10⁹⁸(99-digit number)
57659815939039337801…93061709253577392639
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
5.765 Γ— 10⁹⁸(99-digit number)
57659815939039337801…93061709253577392639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.153 Γ— 10⁹⁹(100-digit number)
11531963187807867560…86123418507154785279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.306 Γ— 10⁹⁹(100-digit number)
23063926375615735120…72246837014309570559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.612 Γ— 10⁹⁹(100-digit number)
46127852751231470241…44493674028619141119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.225 Γ— 10⁹⁹(100-digit number)
92255705502462940482…88987348057238282239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.845 Γ— 10¹⁰⁰(101-digit number)
18451141100492588096…77974696114476564479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.690 Γ— 10¹⁰⁰(101-digit number)
36902282200985176192…55949392228953128959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.380 Γ— 10¹⁰⁰(101-digit number)
73804564401970352385…11898784457906257919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.476 Γ— 10¹⁰¹(102-digit number)
14760912880394070477…23797568915812515839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.952 Γ— 10¹⁰¹(102-digit number)
29521825760788140954…47595137831625031679
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:57,673,184 XPMΒ·at block #6,803,643 Β· updates every 60s
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