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Block #136,110

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 12:38:48 AM Β· Difficulty 9.8146 Β· 6,673,656 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
01bdc035a3394718c8e657eb4f8a8d40b02d7be64a3acd8c0cb899077c93dd03
View on Chainz β†—

Height

#136,110

Difficulty

9.814567

Transactions

2

Size

357 B

Version

2

Bits

09d0877a

Nonce

11,531

Timestamp

8/27/2013, 12:38:48 AM

Confirmations

6,673,656

Mined by

⛏️ P2SHANsvDN5KDUBF83BQczFTri757NjwzDHo7V

Merkle Root

00943596b33ec11308068599be64d86ce19efb809e60b0217387c6fb67b77ee3
Transactions (2)
Coinbase0580cdd010c23e…b370fd524133bc
1 in β†’ 1 out10.3800 XPM109 B
ANsvDN5K…jwzDHo7V
16b741cfce3fc6…83367e5dee7eaf
1 in β†’ 1 out10.4500 XPM158 B
Ad4tU5FR…YoLG8ved
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.

1.647 Γ— 10⁹⁴(95-digit number)
16477107150087247659…10138615772463254399
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
1.647 Γ— 10⁹⁴(95-digit number)
16477107150087247659…10138615772463254399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.295 Γ— 10⁹⁴(95-digit number)
32954214300174495319…20277231544926508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.590 Γ— 10⁹⁴(95-digit number)
65908428600348990639…40554463089853017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁡(96-digit number)
13181685720069798127…81108926179706035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.636 Γ— 10⁹⁡(96-digit number)
26363371440139596255…62217852359412070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.272 Γ— 10⁹⁡(96-digit number)
52726742880279192511…24435704718824140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁢(97-digit number)
10545348576055838502…48871409437648281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.109 Γ— 10⁹⁢(97-digit number)
21090697152111677004…97742818875296563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.218 Γ— 10⁹⁢(97-digit number)
42181394304223354009…95485637750593126399
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:57,722,214 XPMΒ·at block #6,809,765 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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