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Block #137,131

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 3:20:39 PM Β· Difficulty 9.8197 Β· 6,690,173 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0a9d4e5aaafd623f599999a7abde7064710da9c3570d58ab0a7a58bfc145f402
View on Chainz β†—

Height

#137,131

Difficulty

9.819697

Transactions

3

Size

1.87 KB

Version

2

Bits

09d1d7aa

Nonce

8,226

Timestamp

8/27/2013, 3:20:39 PM

Confirmations

6,690,173

Mined by

⛏️ P2SHAKdNqo2eCec6RFFUhCUB3KoVMqq54wHTxk

Merkle Root

3f53404b781600aaa6ab5277758b9419b36a9b3266954f9197974f102655ca25
Transactions (3)
Coinbase95f1678c14d496…3f2432b6894231
1 in β†’ 1 out10.3900 XPM109 B
AKdNqo2e…q54wHTxk
fdca753dff5ec8…465698bc10f10b
1 in β†’ 2 out10.3900 XPM192 B
Ad9V2m9A…MzfKe3hTARjgNH4d…BU7Drh7C
df8026a1c03e4a…77ffa90cd8fbd8
10 in β†’ 1 out21.8937 XPM1.49 KB
Ad1mpGP1…oKBYEVk4
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.

1.974 Γ— 10⁹⁴(95-digit number)
19744637230795347194…35375468345256769839
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
1.974 Γ— 10⁹⁴(95-digit number)
19744637230795347194…35375468345256769839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.948 Γ— 10⁹⁴(95-digit number)
39489274461590694389…70750936690513539679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.897 Γ— 10⁹⁴(95-digit number)
78978548923181388778…41501873381027079359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.579 Γ— 10⁹⁡(96-digit number)
15795709784636277755…83003746762054158719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.159 Γ— 10⁹⁡(96-digit number)
31591419569272555511…66007493524108317439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.318 Γ— 10⁹⁡(96-digit number)
63182839138545111022…32014987048216634879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.263 Γ— 10⁹⁢(97-digit number)
12636567827709022204…64029974096433269759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.527 Γ— 10⁹⁢(97-digit number)
25273135655418044409…28059948192866539519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.054 Γ— 10⁹⁢(97-digit number)
50546271310836088818…56119896385733079039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,862,543 XPMΒ·at block #6,827,303 Β· updates every 60s
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