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Block #2,055,782

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2017, 1:24:15 AM Β· Difficulty 10.8135 Β· 4,760,915 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
72b2f8ceeaa92a048a0fc537c0180862fd1a111a6224d330cd5c9c61ca448345
View on Chainz β†—

Height

#2,055,782

Difficulty

10.813543

Transactions

2

Size

1.28 KB

Version

2

Bits

0ad04462

Nonce

1,119,969,648

Timestamp

4/5/2017, 1:24:15 AM

Confirmations

4,760,915

Mined by

⛏️ P2SHAVU62YsJNMaFvTEhph7J1m58ijUq4tzqDq

Merkle Root

70c2fa0013b330e293d6cbdd892a4f5a9e6b50a8449be1c05d17f5174b66dc8c
Transactions (2)
Coinbase86b7a930257406…c54d16d8df7cb5
1 in β†’ 1 out8.5600 XPM109 B
AVU62YsJ…Uq4tzqDq
af2554c69678aa…c819b7770b2bb6
7 in β†’ 2 out825.1011 XPM1.09 KB
AbAEE55B…t9uajDaqAbhcZzkR…urs5vNpd
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.

3.809 Γ— 10⁹³(94-digit number)
38097736592543969473…38105025869864757759
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
3.809 Γ— 10⁹³(94-digit number)
38097736592543969473…38105025869864757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.619 Γ— 10⁹³(94-digit number)
76195473185087938946…76210051739729515519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁴(95-digit number)
15239094637017587789…52420103479459031039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.047 Γ— 10⁹⁴(95-digit number)
30478189274035175578…04840206958918062079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.095 Γ— 10⁹⁴(95-digit number)
60956378548070351157…09680413917836124159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.219 Γ— 10⁹⁡(96-digit number)
12191275709614070231…19360827835672248319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.438 Γ— 10⁹⁡(96-digit number)
24382551419228140462…38721655671344496639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.876 Γ— 10⁹⁡(96-digit number)
48765102838456280925…77443311342688993279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.753 Γ— 10⁹⁡(96-digit number)
97530205676912561851…54886622685377986559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.950 Γ— 10⁹⁢(97-digit number)
19506041135382512370…09773245370755973119
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:57,777,698 XPMΒ·at block #6,816,696 Β· updates every 60s
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