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Block #346,718

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2014, 5:40:15 PM Β· Difficulty 10.2312 Β· 6,478,173 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
257cfc694bbd161c13e18ba7197f52f6fb3c335d4e57dfcf3810bb4ba3859310
View on Chainz β†—

Height

#346,718

Difficulty

10.231164

Transactions

1

Size

206 B

Version

2

Bits

0a3b2d8f

Nonce

297,950

Timestamp

1/6/2014, 5:40:15 PM

Confirmations

6,478,173

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

832f49e5451b8f73a4d04c7fa8d6f41c1f0a5e12da298bbefc480b85179a397b
Transactions (1)
Coinbase832f49e5451b8f…480b85179a397b
1 in β†’ 1 out9.5400 XPM116 B
AbwWkWZt…kawDhufa
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.

1.512 Γ— 10⁹⁴(95-digit number)
15122168141201959865…43375995040672135039
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
1.512 Γ— 10⁹⁴(95-digit number)
15122168141201959865…43375995040672135039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.512 Γ— 10⁹⁴(95-digit number)
15122168141201959865…43375995040672135041
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
3.024 Γ— 10⁹⁴(95-digit number)
30244336282403919731…86751990081344270079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.024 Γ— 10⁹⁴(95-digit number)
30244336282403919731…86751990081344270081
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
6.048 Γ— 10⁹⁴(95-digit number)
60488672564807839462…73503980162688540159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.048 Γ— 10⁹⁴(95-digit number)
60488672564807839462…73503980162688540161
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
1.209 Γ— 10⁹⁡(96-digit number)
12097734512961567892…47007960325377080319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.209 Γ— 10⁹⁡(96-digit number)
12097734512961567892…47007960325377080321
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
2.419 Γ— 10⁹⁡(96-digit number)
24195469025923135785…94015920650754160639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.419 Γ— 10⁹⁡(96-digit number)
24195469025923135785…94015920650754160641
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:57,843,209 XPMΒ·at block #6,824,890 Β· updates every 60s
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