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Block #154,837

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2013, 10:44:48 PM Β· Difficulty 9.8647 Β· 6,655,299 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a5e7eac7e03bb7629868d8ff1ca536f6a3f0a8a9d2e23e0e6fe234be79f8b6d
View on Chainz β†—

Height

#154,837

Difficulty

9.864670

Transactions

1

Size

197 B

Version

2

Bits

09dd5b06

Nonce

188,823

Timestamp

9/7/2013, 10:44:48 PM

Confirmations

6,655,299

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

5e93df28732d595b731f4d563da2e2917b8f2d72501f6c7c8b9173803a510a64
Transactions (1)
Coinbase5e93df28732d59…9173803a510a64
1 in β†’ 1 out10.2600 XPM109 B
AM9R37qP…hm8dCX8m
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.

5.719 Γ— 10⁸⁸(89-digit number)
57193515844047772268…72081074859889579439
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
5.719 Γ— 10⁸⁸(89-digit number)
57193515844047772268…72081074859889579439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.143 Γ— 10⁸⁹(90-digit number)
11438703168809554453…44162149719779158879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.287 Γ— 10⁸⁹(90-digit number)
22877406337619108907…88324299439558317759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.575 Γ— 10⁸⁹(90-digit number)
45754812675238217815…76648598879116635519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.150 Γ— 10⁸⁹(90-digit number)
91509625350476435630…53297197758233271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.830 Γ— 10⁹⁰(91-digit number)
18301925070095287126…06594395516466542079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.660 Γ— 10⁹⁰(91-digit number)
36603850140190574252…13188791032933084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.320 Γ— 10⁹⁰(91-digit number)
73207700280381148504…26377582065866168319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.464 Γ— 10⁹¹(92-digit number)
14641540056076229700…52755164131732336639
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:57,725,155 XPMΒ·at block #6,810,135 Β· updates every 60s
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