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Block #2,051,674

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 2:27:42 PM Β· Difficulty 10.7215 Β· 4,793,185 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea44c60f82c09ebaf5e4b3de2b4b3e9916af0bf346e0ac567040930c7d1b973f
View on Chainz β†—

Height

#2,051,674

Difficulty

10.721452

Transactions

2

Size

1021 B

Version

2

Bits

0ab8b11a

Nonce

163,976,111

Timestamp

4/3/2017, 2:27:42 PM

Confirmations

4,793,185

Mined by

⛏️ P2SHAPV3gSDwai7iAvtnoaBuWZK1YUwTHnWY2Y

Merkle Root

fb2b6ae93a5dfdaa6e2921085bfe33560d1c1e63885bf8eda94386e29020b070
Transactions (2)
Coinbaseb5760ceecc38ac…525f8b931e2f93
1 in β†’ 1 out8.7000 XPM110 B
APV3gSDw…wTHnWY2Y
fe99472d136645…3cebca267ddd3e
5 in β†’ 2 out1278.5988 XPM820 B
APfCudf4…LjdJA2QGAbAEE55B…t9uajDaq
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.

5.622 Γ— 10⁹⁢(97-digit number)
56225481585158305894…26604610456745464319
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
5.622 Γ— 10⁹⁢(97-digit number)
56225481585158305894…26604610456745464319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.124 Γ— 10⁹⁷(98-digit number)
11245096317031661178…53209220913490928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.249 Γ— 10⁹⁷(98-digit number)
22490192634063322357…06418441826981857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.498 Γ— 10⁹⁷(98-digit number)
44980385268126644715…12836883653963714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.996 Γ— 10⁹⁷(98-digit number)
89960770536253289431…25673767307927429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁸(99-digit number)
17992154107250657886…51347534615854858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁸(99-digit number)
35984308214501315772…02695069231709716479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.196 Γ— 10⁹⁸(99-digit number)
71968616429002631545…05390138463419432959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁹(100-digit number)
14393723285800526309…10780276926838865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.878 Γ— 10⁹⁹(100-digit number)
28787446571601052618…21560553853677731839
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:58,003,284 XPMΒ·at block #6,844,858 Β· updates every 60s
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