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Block #2,030,323

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/20/2017, 1:41:51 AM Β· Difficulty 10.6946 Β· 4,814,566 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
31019c4fb14abce245193adc75f3d2089e583bf6ec50967e3799d5be62cfad6f
View on Chainz β†—

Height

#2,030,323

Difficulty

10.694633

Transactions

1

Size

199 B

Version

2

Bits

0ab1d374

Nonce

1,769,260,336

Timestamp

3/20/2017, 1:41:51 AM

Confirmations

4,814,566

Mined by

⛏️ P2SHAHG8GDqHa2inzdmaRfU3mxoWhtrBp3zjjn

Merkle Root

e089c992da9647e7ee54da36a412882f6deca4daf56086228879329e9c09efd4
Transactions (1)
Coinbasee089c992da9647…79329e9c09efd4
1 in β†’ 1 out8.7300 XPM109 B
AHG8GDqH…rBp3zjjn
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.

5.710 Γ— 10⁹³(94-digit number)
57104353104542556699…12916308831073648199
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
5.710 Γ— 10⁹³(94-digit number)
57104353104542556699…12916308831073648199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.710 Γ— 10⁹³(94-digit number)
57104353104542556699…12916308831073648201
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
1.142 Γ— 10⁹⁴(95-digit number)
11420870620908511339…25832617662147296399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.142 Γ— 10⁹⁴(95-digit number)
11420870620908511339…25832617662147296401
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
2.284 Γ— 10⁹⁴(95-digit number)
22841741241817022679…51665235324294592799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.284 Γ— 10⁹⁴(95-digit number)
22841741241817022679…51665235324294592801
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
4.568 Γ— 10⁹⁴(95-digit number)
45683482483634045359…03330470648589185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.568 Γ— 10⁹⁴(95-digit number)
45683482483634045359…03330470648589185601
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
9.136 Γ— 10⁹⁴(95-digit number)
91366964967268090719…06660941297178371199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.136 Γ— 10⁹⁴(95-digit number)
91366964967268090719…06660941297178371201
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:58,003,527 XPMΒ·at block #6,844,888 Β· updates every 60s
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