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Block #2,306,858

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2017, 4:11:36 AM Β· Difficulty 10.9120 Β· 4,536,194 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
653a3d80926fc0253d73707037876b2d4d3030b628e34ab0104ef987b05fd1b2
View on Chainz β†—

Height

#2,306,858

Difficulty

10.912015

Transactions

1

Size

200 B

Version

2

Bits

0ae979d8

Nonce

311,829,672

Timestamp

9/24/2017, 4:11:36 AM

Confirmations

4,536,194

Mined by

⛏️ P2SHAQszxWzcuUvT7JvauuLAMynKqZnqi8p6Bf

Merkle Root

74baa2213a179afc7d65b78077d45c31db0a82e7350c24eb9491484b13aaac4f
Transactions (1)
Coinbase74baa2213a179a…91484b13aaac4f
1 in β†’ 1 out8.3800 XPM109 B
AQszxWzc…nqi8p6Bf
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.

7.487 Γ— 10⁹⁷(98-digit number)
74870716334662734454…41307105351230095359
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
7.487 Γ— 10⁹⁷(98-digit number)
74870716334662734454…41307105351230095359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.487 Γ— 10⁹⁷(98-digit number)
74870716334662734454…41307105351230095361
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
1.497 Γ— 10⁹⁸(99-digit number)
14974143266932546890…82614210702460190719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.497 Γ— 10⁹⁸(99-digit number)
14974143266932546890…82614210702460190721
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
2.994 Γ— 10⁹⁸(99-digit number)
29948286533865093781…65228421404920381439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.994 Γ— 10⁹⁸(99-digit number)
29948286533865093781…65228421404920381441
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
5.989 Γ— 10⁹⁸(99-digit number)
59896573067730187563…30456842809840762879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.989 Γ— 10⁹⁸(99-digit number)
59896573067730187563…30456842809840762881
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
1.197 Γ— 10⁹⁹(100-digit number)
11979314613546037512…60913685619681525759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.197 Γ— 10⁹⁹(100-digit number)
11979314613546037512…60913685619681525761
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:57,988,774 XPMΒ·at block #6,843,051 Β· updates every 60s
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