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Block #151,046

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 10:42:56 AM Β· Difficulty 9.8594 Β· 6,657,755 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98c64b55175170b8eab8a485444591459594f56a9f887ce55e5306fb718c9d4c
View on Chainz β†—

Height

#151,046

Difficulty

9.859366

Transactions

1

Size

199 B

Version

2

Bits

09dbff66

Nonce

198,446

Timestamp

9/5/2013, 10:42:56 AM

Confirmations

6,657,755

Mined by

⛏️ P2SHAYbFBdKztvJRWUEaa1hwf4Ak9pcf926Mct

Merkle Root

a03a1c7bfdc3420a65b990a069321628999e3875d31ed176e930284655d570c6
Transactions (1)
Coinbasea03a1c7bfdc342…30284655d570c6
1 in β†’ 1 out10.2700 XPM109 B
AYbFBdKz…cf926Mct
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.

2.887 Γ— 10⁹⁴(95-digit number)
28870884951245718394…13305472695984987359
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
2.887 Γ— 10⁹⁴(95-digit number)
28870884951245718394…13305472695984987359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.774 Γ— 10⁹⁴(95-digit number)
57741769902491436789…26610945391969974719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.154 Γ— 10⁹⁡(96-digit number)
11548353980498287357…53221890783939949439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.309 Γ— 10⁹⁡(96-digit number)
23096707960996574715…06443781567879898879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.619 Γ— 10⁹⁡(96-digit number)
46193415921993149431…12887563135759797759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.238 Γ— 10⁹⁡(96-digit number)
92386831843986298863…25775126271519595519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.847 Γ— 10⁹⁢(97-digit number)
18477366368797259772…51550252543039191039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.695 Γ— 10⁹⁢(97-digit number)
36954732737594519545…03100505086078382079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.390 Γ— 10⁹⁢(97-digit number)
73909465475189039090…06201010172156764159
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:57,714,462 XPMΒ·at block #6,808,800 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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