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Block #55,433

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 1:38:44 AM Β· Difficulty 8.9419 Β· 6,754,244 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35bfc36ff2041ef0bf0f2d225e0fa8bc84d541b4dd1edea4bbc9950b1024ff36
View on Chainz β†—

Height

#55,433

Difficulty

8.941872

Transactions

1

Size

199 B

Version

2

Bits

08f11e7f

Nonce

1,952

Timestamp

7/17/2013, 1:38:44 AM

Confirmations

6,754,244

Mined by

⛏️ P2SHAX85bWR1s13thBJxnmv7Zr62AvX2GwLbPj

Merkle Root

953a11c82b9984355eab73cba6b364a2b5eb24c55830cb2c0ed9835c69795a23
Transactions (1)
Coinbase953a11c82b9984…d9835c69795a23
1 in β†’ 1 out12.4900 XPM110 B
AX85bWR1…X2GwLbPj
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.

4.550 Γ— 10⁹¹(92-digit number)
45505720727375557057…16857948480453955839
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
4.550 Γ— 10⁹¹(92-digit number)
45505720727375557057…16857948480453955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.101 Γ— 10⁹¹(92-digit number)
91011441454751114115…33715896960907911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.820 Γ— 10⁹²(93-digit number)
18202288290950222823…67431793921815823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.640 Γ— 10⁹²(93-digit number)
36404576581900445646…34863587843631646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.280 Γ— 10⁹²(93-digit number)
72809153163800891292…69727175687263293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.456 Γ— 10⁹³(94-digit number)
14561830632760178258…39454351374526586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.912 Γ— 10⁹³(94-digit number)
29123661265520356516…78908702749053173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.824 Γ— 10⁹³(94-digit number)
58247322531040713033…57817405498106347519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,721,492 XPMΒ·at block #6,809,676 Β· updates every 60s
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