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Block #680,618

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2014, 8:44:51 PM Β· Difficulty 10.9624 Β· 6,116,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a98428e8920bccba834f9cde3c3a8075b4661d5641212854d63dab6a409ef4e
View on Chainz β†—

Height

#680,618

Difficulty

10.962415

Transactions

2

Size

431 B

Version

2

Bits

0af660cc

Nonce

1,185,381,543

Timestamp

8/16/2014, 8:44:51 PM

Confirmations

6,116,259

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cc821bfaf1db18767caa31a73fd50d2f0737580961058a3502d52764abd9a15c
Transactions (2)
Coinbase0a0fc9f4555540…2c29723dc4c782
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
6e56e81289018d…28369cf2e719c2
1 in β†’ 2 out1.4077 XPM225 B
Ad488TfU…7nkTc86vAXtGFfPj…UY8uHkHy
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.

2.486 Γ— 10⁹⁴(95-digit number)
24862360564935342099…68983694291259753099
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
2.486 Γ— 10⁹⁴(95-digit number)
24862360564935342099…68983694291259753099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.972 Γ— 10⁹⁴(95-digit number)
49724721129870684199…37967388582519506199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.944 Γ— 10⁹⁴(95-digit number)
99449442259741368398…75934777165039012399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.988 Γ— 10⁹⁡(96-digit number)
19889888451948273679…51869554330078024799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.977 Γ— 10⁹⁡(96-digit number)
39779776903896547359…03739108660156049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.955 Γ— 10⁹⁡(96-digit number)
79559553807793094718…07478217320312099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.591 Γ— 10⁹⁢(97-digit number)
15911910761558618943…14956434640624198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.182 Γ— 10⁹⁢(97-digit number)
31823821523117237887…29912869281248396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.364 Γ— 10⁹⁢(97-digit number)
63647643046234475775…59825738562496793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.272 Γ— 10⁹⁷(98-digit number)
12729528609246895155…19651477124993587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.545 Γ— 10⁹⁷(98-digit number)
25459057218493790310…39302954249987174399
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:57,619,032 XPMΒ·at block #6,796,876 Β· updates every 60s
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