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Block #902,616

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2015, 12:13:32 PM Β· Difficulty 10.9396 Β· 5,908,444 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6f25ab2efbfd21ac9e59acb33fdaf71ddd860bfef0af34a86e1c635f4c327394
View on Chainz β†—

Height

#902,616

Difficulty

10.939604

Transactions

2

Size

7.64 KB

Version

2

Bits

0af089e3

Nonce

249,897,854

Timestamp

1/20/2015, 12:13:32 PM

Confirmations

5,908,444

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f67ff62aa2a4582e5003a417311278524ca9ef64a9a05362d24a140001b2dcae
Transactions (2)
Coinbase7be592c7ae9cb0…e1f8fa15ddd3b5
1 in β†’ 1 out8.4200 XPM116 B
ANSXnLY2…Sd25TjkD
40c23a55e3c764…7158f4048ee835
51 in β†’ 2 out203.4100 XPM7.44 KB
AXPkCm4i…AdLMmYemARdb4Ht5…9ngQhLKS
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.

1.106 Γ— 10⁹⁢(97-digit number)
11064618437190756645…12547093401651847519
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
1.106 Γ— 10⁹⁢(97-digit number)
11064618437190756645…12547093401651847519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁢(97-digit number)
22129236874381513291…25094186803303695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.425 Γ— 10⁹⁢(97-digit number)
44258473748763026583…50188373606607390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.851 Γ— 10⁹⁢(97-digit number)
88516947497526053167…00376747213214780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.770 Γ— 10⁹⁷(98-digit number)
17703389499505210633…00753494426429560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.540 Γ— 10⁹⁷(98-digit number)
35406778999010421266…01506988852859120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.081 Γ— 10⁹⁷(98-digit number)
70813557998020842533…03013977705718241279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁸(99-digit number)
14162711599604168506…06027955411436482559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.832 Γ— 10⁹⁸(99-digit number)
28325423199208337013…12055910822872965119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.665 Γ— 10⁹⁸(99-digit number)
56650846398416674027…24111821645745930239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁹(100-digit number)
11330169279683334805…48223643291491860479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,732,585 XPMΒ·at block #6,811,059 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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