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Block #2,232,738

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2017, 8:00:42 PM Β· Difficulty 10.9461 Β· 4,611,302 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3852c6f5969a1eaccd0552bdd386f992c12a6e62da071f95dd795056a63e01bd
View on Chainz β†—

Height

#2,232,738

Difficulty

10.946064

Transactions

2

Size

573 B

Version

2

Bits

0af23146

Nonce

400,731,065

Timestamp

8/1/2017, 8:00:42 PM

Confirmations

4,611,302

Mined by

⛏️ P2SHAYwYFiENyLUDnEsJ4qKCMAugyynMYWz5fN

Merkle Root

cb45769e34c914f508a86fc76aa09cfe6b10567d1c4141a089ea38ce479d594c
Transactions (2)
Coinbasea81d0e21cc3187…585b2b9a1618f2
1 in β†’ 1 out8.3400 XPM109 B
AYwYFiEN…nMYWz5fN
0c4e5f7cb15bfc…257011d6689623
2 in β†’ 2 out1.9500 XPM374 B
ATbraDFx…5zidfhSTAWNTUK6L…5V4GLQzk
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.

6.221 Γ— 10⁹³(94-digit number)
62219782779800580316…40561074800872992639
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
6.221 Γ— 10⁹³(94-digit number)
62219782779800580316…40561074800872992639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.221 Γ— 10⁹³(94-digit number)
62219782779800580316…40561074800872992641
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
1.244 Γ— 10⁹⁴(95-digit number)
12443956555960116063…81122149601745985279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.244 Γ— 10⁹⁴(95-digit number)
12443956555960116063…81122149601745985281
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
2.488 Γ— 10⁹⁴(95-digit number)
24887913111920232126…62244299203491970559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.488 Γ— 10⁹⁴(95-digit number)
24887913111920232126…62244299203491970561
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
4.977 Γ— 10⁹⁴(95-digit number)
49775826223840464253…24488598406983941119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.977 Γ— 10⁹⁴(95-digit number)
49775826223840464253…24488598406983941121
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
9.955 Γ— 10⁹⁴(95-digit number)
99551652447680928506…48977196813967882239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.955 Γ— 10⁹⁴(95-digit number)
99551652447680928506…48977196813967882241
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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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