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Block #919,534

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/2/2015, 6:18:25 AM Β· Difficulty 10.9202 Β· 5,883,923 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a11dfffc6ced4c8b10a1bcb15c2fa961c03738bc8e1ab26dfa98ce0a218c4c7d
View on Chainz β†—

Height

#919,534

Difficulty

10.920186

Transactions

2

Size

729 B

Version

2

Bits

0aeb914d

Nonce

520,215,250

Timestamp

2/2/2015, 6:18:25 AM

Confirmations

5,883,923

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

28393a84416d47fb92a30d1f52e416c582beaa24b2bd4f81507ede6e2cc882bc
Transactions (2)
Coinbasee256279bfdc20f…44cf99f1609f4b
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
124d43e2ec2149…03d879deb3adf6
3 in β†’ 2 out112.3313 XPM522 B
ATzFBw7S…JnmbjfvKATo8D213…FnUe2HYb
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.

1.123 Γ— 10⁹⁸(99-digit number)
11232664847664798203…62327643031789240319
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
1.123 Γ— 10⁹⁸(99-digit number)
11232664847664798203…62327643031789240319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.246 Γ— 10⁹⁸(99-digit number)
22465329695329596407…24655286063578480639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.493 Γ— 10⁹⁸(99-digit number)
44930659390659192815…49310572127156961279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.986 Γ— 10⁹⁸(99-digit number)
89861318781318385631…98621144254313922559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁹(100-digit number)
17972263756263677126…97242288508627845119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.594 Γ— 10⁹⁹(100-digit number)
35944527512527354252…94484577017255690239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.188 Γ— 10⁹⁹(100-digit number)
71889055025054708505…88969154034511380479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.437 Γ— 10¹⁰⁰(101-digit number)
14377811005010941701…77938308069022760959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.875 Γ— 10¹⁰⁰(101-digit number)
28755622010021883402…55876616138045521919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.751 Γ— 10¹⁰⁰(101-digit number)
57511244020043766804…11753232276091043839
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:57,671,683 XPMΒ·at block #6,803,456 Β· updates every 60s
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