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Block #866,461

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/24/2014, 3:01:12 PM Β· Difficulty 10.9627 Β· 5,943,341 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58c6e1f81bec0d703ccbad593360c9addcfb0781c7f719bfec1248eb21c7d187
View on Chainz β†—

Height

#866,461

Difficulty

10.962676

Transactions

2

Size

581 B

Version

2

Bits

0af671ed

Nonce

179,343,404

Timestamp

12/24/2014, 3:01:12 PM

Confirmations

5,943,341

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

148fe879e6dabec8d7f0c9523689cf91bca72b47bb90b07937306a3b8e114430
Transactions (2)
Coinbase42b5d092158105…30e315935724d9
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
ed9922864f306d…b744303dfb4f73
2 in β†’ 2 out478.9860 XPM374 B
ATPbBUz6…9TYXiCMcAGf4bxML…tCqWcVMH
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.

2.868 Γ— 10⁹⁷(98-digit number)
28680214514968631119…26975313396186490879
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
2.868 Γ— 10⁹⁷(98-digit number)
28680214514968631119…26975313396186490879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.736 Γ— 10⁹⁷(98-digit number)
57360429029937262239…53950626792372981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁸(99-digit number)
11472085805987452447…07901253584745963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.294 Γ— 10⁹⁸(99-digit number)
22944171611974904895…15802507169491927039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.588 Γ— 10⁹⁸(99-digit number)
45888343223949809791…31605014338983854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.177 Γ— 10⁹⁸(99-digit number)
91776686447899619583…63210028677967708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.835 Γ— 10⁹⁹(100-digit number)
18355337289579923916…26420057355935416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.671 Γ— 10⁹⁹(100-digit number)
36710674579159847833…52840114711870832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.342 Γ— 10⁹⁹(100-digit number)
73421349158319695666…05680229423741665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.468 Γ— 10¹⁰⁰(101-digit number)
14684269831663939133…11360458847483330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.936 Γ— 10¹⁰⁰(101-digit number)
29368539663327878266…22720917694966661119
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:57,722,497 XPMΒ·at block #6,809,801 Β· updates every 60s
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