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Block #137,616

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 10:01:04 PM Β· Difficulty 9.8228 Β· 6,676,462 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
56203682b3f26132b17a4b18fe531cd9b53588a8dcf66401a981716de434f32c
View on Chainz β†—

Height

#137,616

Difficulty

9.822757

Transactions

1

Size

197 B

Version

2

Bits

09d2a031

Nonce

598,976

Timestamp

8/27/2013, 10:01:04 PM

Confirmations

6,676,462

Mined by

⛏️ P2SHALMTd23CHjiG4kx2mM776gzfXKxCTXJu9f

Merkle Root

655a78b8459e8fe81a98ad50c5dd3411f08894c729438fbd37e5d5a444c8794e
Transactions (1)
Coinbase655a78b8459e8f…e5d5a444c8794e
1 in β†’ 1 out10.3500 XPM109 B
ALMTd23C…xCTXJu9f
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.

1.400 Γ— 10⁹⁰(91-digit number)
14000755169314676645…60171437325223105919
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
1.400 Γ— 10⁹⁰(91-digit number)
14000755169314676645…60171437325223105919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.800 Γ— 10⁹⁰(91-digit number)
28001510338629353290…20342874650446211839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.600 Γ— 10⁹⁰(91-digit number)
56003020677258706581…40685749300892423679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.120 Γ— 10⁹¹(92-digit number)
11200604135451741316…81371498601784847359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.240 Γ— 10⁹¹(92-digit number)
22401208270903482632…62742997203569694719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.480 Γ— 10⁹¹(92-digit number)
44802416541806965264…25485994407139389439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.960 Γ— 10⁹¹(92-digit number)
89604833083613930529…50971988814278778879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.792 Γ— 10⁹²(93-digit number)
17920966616722786105…01943977628557557759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.584 Γ— 10⁹²(93-digit number)
35841933233445572211…03887955257115115519
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:57,756,704 XPMΒ·at block #6,814,077 Β· updates every 60s
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