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Block #1,990,129

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/19/2017, 3:04:30 PM Β· Difficulty 10.7355 Β· 4,825,919 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa16742ae8a9122f700882368799718613075ce11c4b05e64d07caf1fe779743
View on Chainz β†—

Height

#1,990,129

Difficulty

10.735497

Transactions

2

Size

4.13 KB

Version

2

Bits

0abc4985

Nonce

996,621,566

Timestamp

2/19/2017, 3:04:30 PM

Confirmations

4,825,919

Mined by

⛏️ P2SHAZ3qdZecSyiASn9R8gjScJpLY5aqn7WGnK

Merkle Root

4652b162621e29d1db4186f5f80329b4d88677d92d81f355f0959796a0164435
Transactions (2)
Coinbase8d1dfb6e33621e…77a2af92882597
1 in β†’ 1 out8.7100 XPM110 B
AZ3qdZec…aqn7WGnK
219d74958eb19a…cb2782dc16d5a9
27 in β†’ 1 out1460.3250 XPM3.94 KB
AeQtMNpd…o9XTYize
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.

2.901 Γ— 10⁹⁡(96-digit number)
29015161470052366929…81516135450356940799
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
2.901 Γ— 10⁹⁡(96-digit number)
29015161470052366929…81516135450356940799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.803 Γ— 10⁹⁡(96-digit number)
58030322940104733859…63032270900713881599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁢(97-digit number)
11606064588020946771…26064541801427763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.321 Γ— 10⁹⁢(97-digit number)
23212129176041893543…52129083602855526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.642 Γ— 10⁹⁢(97-digit number)
46424258352083787087…04258167205711052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.284 Γ— 10⁹⁢(97-digit number)
92848516704167574174…08516334411422105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁷(98-digit number)
18569703340833514834…17032668822844211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.713 Γ— 10⁹⁷(98-digit number)
37139406681667029669…34065337645688422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.427 Γ— 10⁹⁷(98-digit number)
74278813363334059339…68130675291376844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.485 Γ— 10⁹⁸(99-digit number)
14855762672666811867…36261350582753689599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,772,500 XPMΒ·at block #6,816,047 Β· updates every 60s
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