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Block #574,552

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2014, 9:53:46 AM Β· Difficulty 10.9677 Β· 6,235,582 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ff369a5901b12f851027b86b0bb5ff12c0214cef82819a597b3982d02f3ea165
View on Chainz β†—

Height

#574,552

Difficulty

10.967673

Transactions

1

Size

187 B

Version

2

Bits

0af7b96d

Nonce

7,602

Timestamp

6/3/2014, 9:53:46 AM

Confirmations

6,235,582

Mined by

⛏️ XaSAYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

e89f27c99cbdfb65ccea724af4be428e468d57616ef8f5227fe8322148a8654d
Transactions (1)
Coinbasee89f27c99cbdfb…e8322148a8654d
1 in β†’ 1 out8.3000 XPM96 B
AYCeLhqB…eqGM6KK1
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.

1.726 Γ— 10⁹⁷(98-digit number)
17267937835390060172…90588666923502252399
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
1.726 Γ— 10⁹⁷(98-digit number)
17267937835390060172…90588666923502252399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.453 Γ— 10⁹⁷(98-digit number)
34535875670780120344…81177333847004504799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.907 Γ— 10⁹⁷(98-digit number)
69071751341560240689…62354667694009009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁸(99-digit number)
13814350268312048137…24709335388018019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.762 Γ— 10⁹⁸(99-digit number)
27628700536624096275…49418670776036038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.525 Γ— 10⁹⁸(99-digit number)
55257401073248192551…98837341552072076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁹(100-digit number)
11051480214649638510…97674683104144153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.210 Γ— 10⁹⁹(100-digit number)
22102960429299277020…95349366208288307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.420 Γ— 10⁹⁹(100-digit number)
44205920858598554041…90698732416576614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.841 Γ— 10⁹⁹(100-digit number)
88411841717197108083…81397464833153228799
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:57,725,139 XPMΒ·at block #6,810,133 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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