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Block #772,898

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/17/2014, 4:06:12 PM Β· Difficulty 10.9821 Β· 6,037,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77a450a28ce1717dae61c4b9dcd4f885af353f551135f326edba461050a86422
View on Chainz β†—

Height

#772,898

Difficulty

10.982093

Transactions

2

Size

1.87 KB

Version

2

Bits

0afb6a6c

Nonce

822,170,720

Timestamp

10/17/2014, 4:06:12 PM

Confirmations

6,037,656

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

207e4ac27b47adcd50ae96cd33b659da521faa97c6f2ed910f5c164cb5c5d063
Transactions (2)
Coinbase89db1d5492c855…55e57d28f46f08
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
208c9b209caef9…a9f72fa7b5fcd4
11 in β†’ 2 out13.9720 XPM1.67 KB
AdJF6c71…CWoS2V1UAX8Dmu5K…2D5UKwqj
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.

3.278 Γ— 10⁹⁷(98-digit number)
32781460642335340045…47529923935277998081
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.278 Γ— 10⁹⁷(98-digit number)
32781460642335340045…47529923935277998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.556 Γ— 10⁹⁷(98-digit number)
65562921284670680090…95059847870555996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.311 Γ— 10⁹⁸(99-digit number)
13112584256934136018…90119695741111992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.622 Γ— 10⁹⁸(99-digit number)
26225168513868272036…80239391482223984641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.245 Γ— 10⁹⁸(99-digit number)
52450337027736544072…60478782964447969281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.049 Γ— 10⁹⁹(100-digit number)
10490067405547308814…20957565928895938561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.098 Γ— 10⁹⁹(100-digit number)
20980134811094617629…41915131857791877121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.196 Γ— 10⁹⁹(100-digit number)
41960269622189235258…83830263715583754241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.392 Γ— 10⁹⁹(100-digit number)
83920539244378470516…67660527431167508481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.678 Γ— 10¹⁰⁰(101-digit number)
16784107848875694103…35321054862335016961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.356 Γ— 10¹⁰⁰(101-digit number)
33568215697751388206…70642109724670033921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,728,521 XPMΒ·at block #6,810,553 Β· updates every 60s
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