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Block #1,681,375

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 7:40:10 AM Β· Difficulty 10.7152 Β· 5,163,830 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f45c8b6b8a0d1876fee558df99bb292e8073cb72c5500215b1c6cebe7b8f2c72
View on Chainz β†—

Height

#1,681,375

Difficulty

10.715204

Transactions

1

Size

199 B

Version

2

Bits

0ab7179d

Nonce

944,257,899

Timestamp

7/20/2016, 7:40:10 AM

Confirmations

5,163,830

Mined by

⛏️ P2SHAW98VeEzjQRaocS2ayRmmD23iNGtpzL3Lc

Merkle Root

3b8676f541c46b3593fe73b2fc5ce95048f5cacb967212af635a1c1de867e825
Transactions (1)
Coinbase3b8676f541c46b…5a1c1de867e825
1 in β†’ 1 out8.7000 XPM109 B
AW98VeEz…GtpzL3Lc
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.

8.995 Γ— 10⁹⁴(95-digit number)
89952057417857437007…39735019257247127199
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
8.995 Γ— 10⁹⁴(95-digit number)
89952057417857437007…39735019257247127199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁡(96-digit number)
17990411483571487401…79470038514494254399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁡(96-digit number)
35980822967142974802…58940077028988508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.196 Γ— 10⁹⁡(96-digit number)
71961645934285949605…17880154057977017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁢(97-digit number)
14392329186857189921…35760308115954035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.878 Γ— 10⁹⁢(97-digit number)
28784658373714379842…71520616231908070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.756 Γ— 10⁹⁢(97-digit number)
57569316747428759684…43041232463816140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁷(98-digit number)
11513863349485751936…86082464927632281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.302 Γ— 10⁹⁷(98-digit number)
23027726698971503873…72164929855264563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.605 Γ— 10⁹⁷(98-digit number)
46055453397943007747…44329859710529126399
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:58,006,072 XPMΒ·at block #6,845,204 Β· updates every 60s
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