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Block #256,295

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/11/2013, 6:03:24 PM Β· Difficulty 9.9752 Β· 6,552,688 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
12baf9cee2fbd140a8b87b91af7a9ef3ce13425e60e54f9b0a5c50e6b2664772
View on Chainz β†—

Height

#256,295

Difficulty

9.975158

Transactions

2

Size

3.31 KB

Version

2

Bits

09f9a3ef

Nonce

5,344

Timestamp

11/11/2013, 6:03:24 PM

Confirmations

6,552,688

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

5419dca1ba2551ba5dc4316fafd205c720092710d3211259d41be35f2f3629fa
Transactions (2)
Coinbasebb68ca1499f8fe…498f905ed4889e
1 in β†’ 2 out10.0700 XPM140 B
AdGRRh1e…QmctLb24Abiw8n3q…ZnZfgvQW
fce0bf2f805e72…cc47322680c47e
21 in β†’ 1 out300.0000 XPM3.08 KB
AXc99h1F…o4ftNX3T
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.

3.985 Γ— 10⁹⁴(95-digit number)
39858732121518043827…92565065393914169669
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
3.985 Γ— 10⁹⁴(95-digit number)
39858732121518043827…92565065393914169669
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.985 Γ— 10⁹⁴(95-digit number)
39858732121518043827…92565065393914169671
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
7.971 Γ— 10⁹⁴(95-digit number)
79717464243036087654…85130130787828339339
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.971 Γ— 10⁹⁴(95-digit number)
79717464243036087654…85130130787828339341
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
1.594 Γ— 10⁹⁡(96-digit number)
15943492848607217530…70260261575656678679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.594 Γ— 10⁹⁡(96-digit number)
15943492848607217530…70260261575656678681
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
3.188 Γ— 10⁹⁡(96-digit number)
31886985697214435061…40520523151313357359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.188 Γ— 10⁹⁡(96-digit number)
31886985697214435061…40520523151313357361
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
6.377 Γ— 10⁹⁡(96-digit number)
63773971394428870123…81041046302626714719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.377 Γ— 10⁹⁡(96-digit number)
63773971394428870123…81041046302626714721
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:57,715,921 XPMΒ·at block #6,808,982 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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