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Block #278,730

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 2:34:56 AM Β· Difficulty 9.9697 Β· 6,548,224 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea3fc58fd906df9448cd84812292277985a9a60189bbdb98817d8d327c7779bf
View on Chainz β†—

Height

#278,730

Difficulty

9.969703

Transactions

1

Size

209 B

Version

2

Bits

09f83e6d

Nonce

1,766

Timestamp

11/28/2013, 2:34:56 AM

Confirmations

6,548,224

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

0f07823a15f064f5b31c006774aba27b6333b3de142d5df167efd119857d13c2
Transactions (1)
Coinbase0f07823a15f064…efd119857d13c2
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.738 Γ— 10¹⁰³(104-digit number)
17383612384360826613…45800633073763614719
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
1.738 Γ— 10¹⁰³(104-digit number)
17383612384360826613…45800633073763614719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.476 Γ— 10¹⁰³(104-digit number)
34767224768721653227…91601266147527229439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.953 Γ— 10¹⁰³(104-digit number)
69534449537443306454…83202532295054458879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.390 Γ— 10¹⁰⁴(105-digit number)
13906889907488661290…66405064590108917759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.781 Γ— 10¹⁰⁴(105-digit number)
27813779814977322581…32810129180217835519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.562 Γ— 10¹⁰⁴(105-digit number)
55627559629954645163…65620258360435671039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.112 Γ— 10¹⁰⁡(106-digit number)
11125511925990929032…31240516720871342079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.225 Γ— 10¹⁰⁡(106-digit number)
22251023851981858065…62481033441742684159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.450 Γ— 10¹⁰⁡(106-digit number)
44502047703963716130…24962066883485368319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.900 Γ— 10¹⁰⁡(106-digit number)
89004095407927432261…49924133766970736639
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:57,859,808 XPMΒ·at block #6,826,953 Β· updates every 60s
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