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Block #1,249,629

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/23/2015, 12:59:27 PM Β· Difficulty 10.7676 Β· 5,568,060 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
002c2f897f8e46abd84566d709ffd77b6afe59e04a2c970f32fa555b769a0b41
View on Chainz β†—

Height

#1,249,629

Difficulty

10.767594

Transactions

2

Size

1.97 KB

Version

2

Bits

0ac48107

Nonce

1,556,148,254

Timestamp

9/23/2015, 12:59:27 PM

Confirmations

5,568,060

Mined by

⛏️ P2SHANLedeUaVNfQbU1kyWDLMi2WtcLg2LgDkP

Merkle Root

d523c0a50808d372a0086fef18af407853711170986ea2b9238aba4514e38ae2
Transactions (2)
Coinbasecfc3be54d243e7…bfbbd602d99a47
1 in β†’ 1 out8.6300 XPM110 B
ANLedeUa…Lg2LgDkP
6b7dc55f8ccb5a…213bc76816606e
12 in β†’ 1 out169.5394 XPM1.78 KB
AQHE5e6H…xDwU3vYU
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.

8.250 Γ— 10⁹³(94-digit number)
82509525603776261285…16507036250904039059
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
8.250 Γ— 10⁹³(94-digit number)
82509525603776261285…16507036250904039059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁴(95-digit number)
16501905120755252257…33014072501808078119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.300 Γ— 10⁹⁴(95-digit number)
33003810241510504514…66028145003616156239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.600 Γ— 10⁹⁴(95-digit number)
66007620483021009028…32056290007232312479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁡(96-digit number)
13201524096604201805…64112580014464624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.640 Γ— 10⁹⁡(96-digit number)
26403048193208403611…28225160028929249919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.280 Γ— 10⁹⁡(96-digit number)
52806096386416807222…56450320057858499839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁢(97-digit number)
10561219277283361444…12900640115716999679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.112 Γ— 10⁹⁢(97-digit number)
21122438554566722889…25801280231433999359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.224 Γ— 10⁹⁢(97-digit number)
42244877109133445778…51602560462867998719
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:57,785,570 XPMΒ·at block #6,817,688 Β· updates every 60s
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