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Block #778,541

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2014, 11:22:50 PM Β· Difficulty 10.9802 Β· 6,023,869 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0abe3312ffd736638b355ffdc3d4801a1869d163a4d56bb8ff5783817eba9c3d
View on Chainz β†—

Height

#778,541

Difficulty

10.980194

Transactions

2

Size

42.77 KB

Version

2

Bits

0afaee06

Nonce

897,942,605

Timestamp

10/21/2014, 11:22:50 PM

Confirmations

6,023,869

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

54d216ba771ef86b50ed11b29e3041a3d7ab77eb4253e11005a1d771ca3da80c
Transactions (2)
Coinbase5e52700c2625a9…435bae40c60d71
1 in β†’ 1 out8.7400 XPM116 B
ANSXnLY2…Sd25TjkD
0d8e4fdd49a8f2…d938a50a2ee42c
294 in β†’ 2 out505.2794 XPM42.56 KB
Ae8VnHm6…PEUBLVDpAVcx4BnE…omggwQuL
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.

4.120 Γ— 10⁹⁴(95-digit number)
41200520341702420320…10833237483809663649
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
4.120 Γ— 10⁹⁴(95-digit number)
41200520341702420320…10833237483809663649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.240 Γ— 10⁹⁴(95-digit number)
82401040683404840640…21666474967619327299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.648 Γ— 10⁹⁡(96-digit number)
16480208136680968128…43332949935238654599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.296 Γ— 10⁹⁡(96-digit number)
32960416273361936256…86665899870477309199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.592 Γ— 10⁹⁡(96-digit number)
65920832546723872512…73331799740954618399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁢(97-digit number)
13184166509344774502…46663599481909236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.636 Γ— 10⁹⁢(97-digit number)
26368333018689549004…93327198963818473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.273 Γ— 10⁹⁢(97-digit number)
52736666037379098009…86654397927636947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁷(98-digit number)
10547333207475819601…73308795855273894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.109 Γ— 10⁹⁷(98-digit number)
21094666414951639203…46617591710547788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.218 Γ— 10⁹⁷(98-digit number)
42189332829903278407…93235183421095577599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,663,286 XPMΒ·at block #6,802,409 Β· updates every 60s
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