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Block #1,681,703

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 12:40:52 PM Β· Difficulty 10.7166 Β· 5,126,413 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
571066f4f4a1637cf02726e13436ff3c4e34240565dc1ea23cfd95852be504ab
View on Chainz β†—

Height

#1,681,703

Difficulty

10.716587

Transactions

2

Size

17.62 KB

Version

2

Bits

0ab77238

Nonce

669,405,655

Timestamp

7/20/2016, 12:40:52 PM

Confirmations

5,126,413

Mined by

⛏️ P2SHALbBN8LzEL6y7U2byjv3WWgHwsCGjgcNWF

Merkle Root

cb5e36ee9d51b59269bee8194c581086c0311b2bf59bb242da756be5dbd65446
Transactions (2)
Coinbaseb1a9933798fa39…40495df2704b9f
1 in β†’ 1 out8.8700 XPM109 B
ALbBN8Lz…CGjgcNWF
dd88088f622f49…2fd2d15d2ff9a6
120 in β†’ 2 out22.1750 XPM17.42 KB
AGyiGjWR…yy2Gk1HVAdqtMD9a…Ln1Rw6hG
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.

2.097 Γ— 10⁹⁴(95-digit number)
20974840410617729446…52117381822750627839
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
2.097 Γ— 10⁹⁴(95-digit number)
20974840410617729446…52117381822750627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.194 Γ— 10⁹⁴(95-digit number)
41949680821235458892…04234763645501255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.389 Γ— 10⁹⁴(95-digit number)
83899361642470917784…08469527291002511359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.677 Γ— 10⁹⁡(96-digit number)
16779872328494183556…16939054582005022719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.355 Γ— 10⁹⁡(96-digit number)
33559744656988367113…33878109164010045439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.711 Γ— 10⁹⁡(96-digit number)
67119489313976734227…67756218328020090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁢(97-digit number)
13423897862795346845…35512436656040181759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.684 Γ— 10⁹⁢(97-digit number)
26847795725590693691…71024873312080363519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.369 Γ— 10⁹⁢(97-digit number)
53695591451181387382…42049746624160727039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁷(98-digit number)
10739118290236277476…84099493248321454079
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:57,708,976 XPMΒ·at block #6,808,115 Β· updates every 60s
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