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Block #1,612,988

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2016, 11:29:43 PM Β· Difficulty 10.6009 Β· 5,203,609 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97a7b2aed142f4530346264325c46a06a577f4a432e99915ab725dfe5ba16df3
View on Chainz β†—

Height

#1,612,988

Difficulty

10.600903

Transactions

2

Size

8.33 KB

Version

2

Bits

0a99d4ce

Nonce

828,779,148

Timestamp

6/3/2016, 11:29:43 PM

Confirmations

5,203,609

Mined by

⛏️ P2SHANMwEVmsDyZAAQo32niDeCEcabvM49gzHF

Merkle Root

6034cb331b869250816b0fcfd50650c6abc6700d2f25b7ee2955282ffedd922d
Transactions (2)
Coinbase87f1ed7c0c35d8…fe24c479daa8e3
1 in β†’ 1 out9.0200 XPM110 B
ANMwEVms…vM49gzHF
dec52d923c6515…8918527cfb1510
56 in β†’ 1 out3.0715 XPM8.14 KB
AV2V1Fp8…jkkNUxTV
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.

2.940 Γ— 10⁹⁡(96-digit number)
29403708866694707042…57599351015490135039
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
2.940 Γ— 10⁹⁡(96-digit number)
29403708866694707042…57599351015490135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.880 Γ— 10⁹⁡(96-digit number)
58807417733389414084…15198702030980270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁢(97-digit number)
11761483546677882816…30397404061960540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁢(97-digit number)
23522967093355765633…60794808123921080319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.704 Γ— 10⁹⁢(97-digit number)
47045934186711531267…21589616247842160639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.409 Γ— 10⁹⁢(97-digit number)
94091868373423062534…43179232495684321279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁷(98-digit number)
18818373674684612506…86358464991368642559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.763 Γ— 10⁹⁷(98-digit number)
37636747349369225013…72716929982737285119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.527 Γ— 10⁹⁷(98-digit number)
75273494698738450027…45433859965474570239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.505 Γ— 10⁹⁸(99-digit number)
15054698939747690005…90867719930949140479
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:57,776,901 XPMΒ·at block #6,816,596 Β· updates every 60s
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