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Block #1,772,322

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2016, 2:10:46 AM Β· Difficulty 10.7476 Β· 5,032,489 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a91689c433fdeb43886c4e107a9136bdb6d0d5e2c14a7891e7434dd3b8de5b5
View on Chainz β†—

Height

#1,772,322

Difficulty

10.747606

Transactions

2

Size

390 B

Version

2

Bits

0abf6313

Nonce

267,254,727

Timestamp

9/21/2016, 2:10:46 AM

Confirmations

5,032,489

Mined by

⛏️ P2SHAKuEVxD3CD4owkG42e3VAVuLqhNZiXdvb9

Merkle Root

c6bc881a67b29c2da043e434d6adc249a28e8d51d6c742928deddea810547562
Transactions (2)
Coinbaseeb2a8dc40daf04…9ad1f383e5986d
1 in β†’ 1 out8.6500 XPM109 B
AKuEVxD3…NZiXdvb9
773f5f2fe2b91b…a10d043970be4b
1 in β†’ 1 out3.9900 XPM192 B
Acso9ZA6…KzouUva2
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.

3.795 Γ— 10⁹³(94-digit number)
37957534922542501713…45494795376114089731
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.795 Γ— 10⁹³(94-digit number)
37957534922542501713…45494795376114089731
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.591 Γ— 10⁹³(94-digit number)
75915069845085003426…90989590752228179461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.518 Γ— 10⁹⁴(95-digit number)
15183013969017000685…81979181504456358921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.036 Γ— 10⁹⁴(95-digit number)
30366027938034001370…63958363008912717841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.073 Γ— 10⁹⁴(95-digit number)
60732055876068002741…27916726017825435681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.214 Γ— 10⁹⁡(96-digit number)
12146411175213600548…55833452035650871361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.429 Γ— 10⁹⁡(96-digit number)
24292822350427201096…11666904071301742721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.858 Γ— 10⁹⁡(96-digit number)
48585644700854402193…23333808142603485441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.717 Γ— 10⁹⁡(96-digit number)
97171289401708804386…46667616285206970881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.943 Γ— 10⁹⁢(97-digit number)
19434257880341760877…93335232570413941761
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,682,556 XPMΒ·at block #6,804,810 Β· updates every 60s
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