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Block #106,748

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2013, 4:18:25 AM Β· Difficulty 9.6145 Β· 6,720,551 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5aeb551de0bb9f1c0e28232e38ebe0f478d1bb4a5537cc87e76dc45c1f2cb691
View on Chainz β†—

Height

#106,748

Difficulty

9.614458

Transactions

1

Size

200 B

Version

2

Bits

099d4d25

Nonce

94,073

Timestamp

8/9/2013, 4:18:25 AM

Confirmations

6,720,551

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

89e2d07b9510ce83db9d26af0dabde10826f60c1d609e8beda627e8b597824aa
Transactions (1)
Coinbase89e2d07b9510ce…627e8b597824aa
1 in β†’ 1 out10.8000 XPM109 B
AX99MLNm…vtidqEwE
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.

5.807 Γ— 10⁹⁷(98-digit number)
58071461953626603714…82029901943173646719
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
5.807 Γ— 10⁹⁷(98-digit number)
58071461953626603714…82029901943173646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁸(99-digit number)
11614292390725320742…64059803886347293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.322 Γ— 10⁹⁸(99-digit number)
23228584781450641485…28119607772694586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.645 Γ— 10⁹⁸(99-digit number)
46457169562901282971…56239215545389173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.291 Γ— 10⁹⁸(99-digit number)
92914339125802565943…12478431090778347519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁹(100-digit number)
18582867825160513188…24956862181556695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁹(100-digit number)
37165735650321026377…49913724363113390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.433 Γ— 10⁹⁹(100-digit number)
74331471300642052754…99827448726226780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.486 Γ— 10¹⁰⁰(101-digit number)
14866294260128410550…99654897452453560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.973 Γ— 10¹⁰⁰(101-digit number)
29732588520256821101…99309794904907120639
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:57,862,502 XPMΒ·at block #6,827,298 Β· updates every 60s
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