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Block #77,453

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2013, 10:22:04 AM Β· Difficulty 9.1728 Β· 6,733,437 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6729e42a7e59fe217ee923a489150e67ef1a2bc637be4d333b87b2aa80a0dfd9
View on Chainz β†—

Height

#77,453

Difficulty

9.172789

Transactions

2

Size

357 B

Version

2

Bits

092c3beb

Nonce

172

Timestamp

7/22/2013, 10:22:04 AM

Confirmations

6,733,437

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

0e94aa0b4f50840801ca86177dd979cb3a9c8d8e309c05ad7211e4f4cc54f18f
Transactions (2)
Coinbasec3e6b0a8f8de16…ca3179e1dd2f7f
1 in β†’ 1 out11.8800 XPM110 B
AGCUbq6M…QSxWg1oL
35729ecab08ed7…1bc83b29beb738
1 in β†’ 1 out12.3500 XPM159 B
Af1Wiv6Z…L4fg3Jrd
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.

9.927 Γ— 10⁸⁹(90-digit number)
99270550277553138916…21711781907010916099
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
9.927 Γ— 10⁸⁹(90-digit number)
99270550277553138916…21711781907010916099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.985 Γ— 10⁹⁰(91-digit number)
19854110055510627783…43423563814021832199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.970 Γ— 10⁹⁰(91-digit number)
39708220111021255566…86847127628043664399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.941 Γ— 10⁹⁰(91-digit number)
79416440222042511133…73694255256087328799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.588 Γ— 10⁹¹(92-digit number)
15883288044408502226…47388510512174657599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.176 Γ— 10⁹¹(92-digit number)
31766576088817004453…94777021024349315199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.353 Γ— 10⁹¹(92-digit number)
63533152177634008906…89554042048698630399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.270 Γ— 10⁹²(93-digit number)
12706630435526801781…79108084097397260799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.541 Γ— 10⁹²(93-digit number)
25413260871053603562…58216168194794521599
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:57,731,218 XPMΒ·at block #6,810,889 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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