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Block #2,088,399

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2017, 7:44:09 AM Β· Difficulty 10.8754 Β· 4,744,283 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7db93cd2cd2a001d714fda98b0e26631c7adf48f3a4c1049a3487d2f30f881f4
View on Chainz β†—

Height

#2,088,399

Difficulty

10.875412

Transactions

2

Size

426 B

Version

2

Bits

0ae01b04

Nonce

848,029,655

Timestamp

4/26/2017, 7:44:09 AM

Confirmations

4,744,283

Mined by

⛏️ P2SHAHbQ1KBM61zRCzpXBzVW1fVzVbx94r9qPD

Merkle Root

7d37a32eb8cf83603b58bc22d00a05bf567cfc670047c73947bdecfa6441bd78
Transactions (2)
Coinbase062a9b55bd8379…d39de896a06e80
1 in β†’ 1 out8.4500 XPM109 B
AHbQ1KBM…x94r9qPD
84741a19a02e33…ba35fce0f7074e
1 in β†’ 2 out92712.7368 XPM227 B
AbnKtNey…gxnW4PjwAJPmZX4j…evDGLJrm
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.

1.328 Γ— 10⁹⁴(95-digit number)
13280960567003427768…13236427221626625239
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.328 Γ— 10⁹⁴(95-digit number)
13280960567003427768…13236427221626625239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.328 Γ— 10⁹⁴(95-digit number)
13280960567003427768…13236427221626625241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁴(95-digit number)
26561921134006855536…26472854443253250479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.656 Γ— 10⁹⁴(95-digit number)
26561921134006855536…26472854443253250481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.312 Γ— 10⁹⁴(95-digit number)
53123842268013711073…52945708886506500959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.312 Γ— 10⁹⁴(95-digit number)
53123842268013711073…52945708886506500961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁡(96-digit number)
10624768453602742214…05891417773013001919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.062 Γ— 10⁹⁡(96-digit number)
10624768453602742214…05891417773013001921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.124 Γ— 10⁹⁡(96-digit number)
21249536907205484429…11782835546026003839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.124 Γ— 10⁹⁡(96-digit number)
21249536907205484429…11782835546026003841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,905,610 XPMΒ·at block #6,832,681 Β· updates every 60s
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