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Block #1,534,676

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 9:53:21 AM Β· Difficulty 10.6176 Β· 5,274,274 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a6ad2ee6d4f15f24598c0d675f7910fc6a28e3b4c364e7f5eefa3fedf54820f9
View on Chainz β†—

Height

#1,534,676

Difficulty

10.617632

Transactions

4

Size

22.45 KB

Version

2

Bits

0a9e1d21

Nonce

914,159,394

Timestamp

4/10/2016, 9:53:21 AM

Confirmations

5,274,274

Mined by

⛏️ P2SHAbhXp6aTg8bK3tmzkgitADKuX8P5MDpKgj

Merkle Root

7778be0b562e7a65275848cf6a38962303d0bd11d2930ac0d2b5e4957d716ae1
Transactions (4)
Coinbase52b57b10e2da82…6b62e2a52d7587
1 in β†’ 1 out9.1000 XPM110 B
AbhXp6aT…P5MDpKgj
8814c1a2cfcbe4…60a12afd68353a
51 in β†’ 1 out669.6142 XPM7.42 KB
AVkT4ta4…9t6omqyF
83db37ec4e571b…2ff027210f6e92
51 in β†’ 1 out3055.9695 XPM7.42 KB
ANDYUn2a…bc3UwjPK
61466b6353c0d4…01d848ed9c78a6
51 in β†’ 1 out346.9097 XPM7.42 KB
ARVtLE1a…rSH37Ps9
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.

9.376 Γ— 10⁹³(94-digit number)
93763415773708952785…38544319405961441059
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
9.376 Γ— 10⁹³(94-digit number)
93763415773708952785…38544319405961441059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.875 Γ— 10⁹⁴(95-digit number)
18752683154741790557…77088638811922882119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.750 Γ— 10⁹⁴(95-digit number)
37505366309483581114…54177277623845764239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.501 Γ— 10⁹⁴(95-digit number)
75010732618967162228…08354555247691528479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁡(96-digit number)
15002146523793432445…16709110495383056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.000 Γ— 10⁹⁡(96-digit number)
30004293047586864891…33418220990766113919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.000 Γ— 10⁹⁡(96-digit number)
60008586095173729782…66836441981532227839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.200 Γ— 10⁹⁢(97-digit number)
12001717219034745956…33672883963064455679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.400 Γ— 10⁹⁢(97-digit number)
24003434438069491912…67345767926128911359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.800 Γ— 10⁹⁢(97-digit number)
48006868876138983825…34691535852257822719
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:57,715,652 XPMΒ·at block #6,808,949 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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