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Block #135,354

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 2:05:13 PM Β· Difficulty 9.8100 Β· 6,660,753 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92b08c52f7e9d73d147736e3b7fad055139de2cba01be08fb2eb18dbbf190709
View on Chainz β†—

Height

#135,354

Difficulty

9.809985

Transactions

1

Size

200 B

Version

2

Bits

09cf5b33

Nonce

14,397

Timestamp

8/26/2013, 2:05:13 PM

Confirmations

6,660,753

Mined by

⛏️ P2SHANTa1K9uo2tZAfCrKshhg4zYQXNvg3kaVt

Merkle Root

6e5e7c3bf85dd9896f6322d34146bf865e82933ea37c251d77eea9498a088d39
Transactions (1)
Coinbase6e5e7c3bf85dd9…eea9498a088d39
1 in β†’ 1 out10.3800 XPM110 B
ANTa1K9u…Nvg3kaVt
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.

7.248 Γ— 10⁹⁴(95-digit number)
72486064441017099748…34715326992076963839
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
7.248 Γ— 10⁹⁴(95-digit number)
72486064441017099748…34715326992076963839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁡(96-digit number)
14497212888203419949…69430653984153927679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.899 Γ— 10⁹⁡(96-digit number)
28994425776406839899…38861307968307855359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.798 Γ— 10⁹⁡(96-digit number)
57988851552813679799…77722615936615710719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁢(97-digit number)
11597770310562735959…55445231873231421439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁢(97-digit number)
23195540621125471919…10890463746462842879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.639 Γ— 10⁹⁢(97-digit number)
46391081242250943839…21780927492925685759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.278 Γ— 10⁹⁢(97-digit number)
92782162484501887678…43561854985851371519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.855 Γ— 10⁹⁷(98-digit number)
18556432496900377535…87123709971702743039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.711 Γ— 10⁹⁷(98-digit number)
37112864993800755071…74247419943405486079
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:57,612,850 XPMΒ·at block #6,796,106 Β· updates every 60s
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