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Block #119,240

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2013, 8:43:22 AM Β· Difficulty 9.7489 Β· 6,687,318 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a1de360ecc8d69625b5a389e2e59995a042bfe633f06a148d1524d6c8581a40
View on Chainz β†—

Height

#119,240

Difficulty

9.748857

Transactions

2

Size

471 B

Version

2

Bits

09bfb519

Nonce

508,312

Timestamp

8/16/2013, 8:43:22 AM

Confirmations

6,687,318

Mined by

⛏️ P2SHAbmY1vQu9ja99Jg9KL3bMyCPpobpyjgT4i

Merkle Root

d9470828e42f18c8f63685004d0513b8cd4e46148a178d7e42049d3858a54b45
Transactions (2)
Coinbaseab9e6ace8a6ad5…f318941e4ac44f
1 in β†’ 1 out10.5200 XPM109 B
AbmY1vQu…bpyjgT4i
c5fd55dc96e8ef…e1dc11b1a83520
2 in β†’ 1 out21.0400 XPM271 B
AVXpXMS3…dbsyn72W
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.

2.588 Γ— 10⁹⁢(97-digit number)
25885213131058529189…12404129012849188479
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
2.588 Γ— 10⁹⁢(97-digit number)
25885213131058529189…12404129012849188479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.177 Γ— 10⁹⁢(97-digit number)
51770426262117058378…24808258025698376959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁷(98-digit number)
10354085252423411675…49616516051396753919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.070 Γ— 10⁹⁷(98-digit number)
20708170504846823351…99233032102793507839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.141 Γ— 10⁹⁷(98-digit number)
41416341009693646702…98466064205587015679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.283 Γ— 10⁹⁷(98-digit number)
82832682019387293405…96932128411174031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.656 Γ— 10⁹⁸(99-digit number)
16566536403877458681…93864256822348062719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.313 Γ— 10⁹⁸(99-digit number)
33133072807754917362…87728513644696125439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.626 Γ— 10⁹⁸(99-digit number)
66266145615509834724…75457027289392250879
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:57,696,559 XPMΒ·at block #6,806,557 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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