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Block #86,994

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2013, 1:17:16 PM Β· Difficulty 9.2846 Β· 6,708,860 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
27815c913e74479c46a5eb607631d4933c94bc83006ae6e8ce53f1615c5c7e64
View on Chainz β†—

Height

#86,994

Difficulty

9.284636

Transactions

2

Size

618 B

Version

2

Bits

0948dde1

Nonce

6,349,878

Timestamp

7/28/2013, 1:17:16 PM

Confirmations

6,708,860

Mined by

⛏️ P2SHAXBqjuvD9u4S2EX4KbqkDDVUde5k8YSwit

Merkle Root

66d869d897994b77582c4ba4f0f33430297dda860dae336654555470e4ea03ff
Transactions (2)
Coinbasea19460ac19a4ad…a9b00559d8566b
1 in β†’ 1 out11.5900 XPM109 B
AXBqjuvD…5k8YSwit
3d6294fe11f53d…94e8dc25940419
3 in β†’ 2 out35.3200 XPM420 B
AGyxFWV2…Rnu4qKbjAFtap2en…4d4n6Nrg
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.

1.367 Γ— 10⁹²(93-digit number)
13670177173745752547…63147674587619534259
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
1.367 Γ— 10⁹²(93-digit number)
13670177173745752547…63147674587619534259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.734 Γ— 10⁹²(93-digit number)
27340354347491505095…26295349175239068519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.468 Γ— 10⁹²(93-digit number)
54680708694983010190…52590698350478137039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.093 Γ— 10⁹³(94-digit number)
10936141738996602038…05181396700956274079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.187 Γ— 10⁹³(94-digit number)
21872283477993204076…10362793401912548159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.374 Γ— 10⁹³(94-digit number)
43744566955986408152…20725586803825096319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.748 Γ— 10⁹³(94-digit number)
87489133911972816304…41451173607650192639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.749 Γ— 10⁹⁴(95-digit number)
17497826782394563260…82902347215300385279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.499 Γ— 10⁹⁴(95-digit number)
34995653564789126521…65804694430600770559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,610,918 XPMΒ·at block #6,795,853 Β· updates every 60s
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