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Block #157,872

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 10:35:14 PM Β· Difficulty 9.8691 Β· 6,646,441 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d9d1a7c16439204743dccf2b4995cc35a4f7bda3b65ac0cb7317a68efa0fbf6e
View on Chainz β†—

Height

#157,872

Difficulty

9.869141

Transactions

1

Size

198 B

Version

2

Bits

09de7fff

Nonce

443,651

Timestamp

9/9/2013, 10:35:14 PM

Confirmations

6,646,441

Mined by

⛏️ P2SHAQE5juVGf2GjfXcDEExb1YTp8cv2LcRcDH

Merkle Root

725b68f42d20b1d5f0d5394e9ba2bb2e64ff1b58239617fb34ac4a656891b632
Transactions (1)
Coinbase725b68f42d20b1…ac4a656891b632
1 in β†’ 1 out10.2500 XPM109 B
AQE5juVG…v2LcRcDH
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.

2.047 Γ— 10⁹²(93-digit number)
20474427631737215887…29327049862958142721
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
2.047 Γ— 10⁹²(93-digit number)
20474427631737215887…29327049862958142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.094 Γ— 10⁹²(93-digit number)
40948855263474431774…58654099725916285441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.189 Γ— 10⁹²(93-digit number)
81897710526948863549…17308199451832570881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.637 Γ— 10⁹³(94-digit number)
16379542105389772709…34616398903665141761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.275 Γ— 10⁹³(94-digit number)
32759084210779545419…69232797807330283521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.551 Γ— 10⁹³(94-digit number)
65518168421559090839…38465595614660567041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.310 Γ— 10⁹⁴(95-digit number)
13103633684311818167…76931191229321134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.620 Γ— 10⁹⁴(95-digit number)
26207267368623636335…53862382458642268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.241 Γ— 10⁹⁴(95-digit number)
52414534737247272671…07724764917284536321
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,678,557 XPMΒ·at block #6,804,312 Β· updates every 60s
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