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Block #320,767

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2013, 9:14:25 PM Β· Difficulty 10.1858 Β· 6,515,985 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ad15f8551439a6ec48e9fa1e005b63619ed126be0fcc7890365883f280d918a
View on Chainz β†—

Height

#320,767

Difficulty

10.185767

Transactions

1

Size

207 B

Version

2

Bits

0a2f8e6b

Nonce

27,462

Timestamp

12/19/2013, 9:14:25 PM

Confirmations

6,515,985

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

87b41298beed62a9addbb68d08ab80775359c94bbcc33cee96d281ba67a8fd15
Transactions (1)
Coinbase87b41298beed62…d281ba67a8fd15
1 in β†’ 1 out9.6200 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.

8.030 Γ— 10⁹⁢(97-digit number)
80301596976258754760…62602370908585411599
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
8.030 Γ— 10⁹⁢(97-digit number)
80301596976258754760…62602370908585411599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.030 Γ— 10⁹⁢(97-digit number)
80301596976258754760…62602370908585411601
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
1.606 Γ— 10⁹⁷(98-digit number)
16060319395251750952…25204741817170823199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.606 Γ— 10⁹⁷(98-digit number)
16060319395251750952…25204741817170823201
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
3.212 Γ— 10⁹⁷(98-digit number)
32120638790503501904…50409483634341646399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.212 Γ— 10⁹⁷(98-digit number)
32120638790503501904…50409483634341646401
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
6.424 Γ— 10⁹⁷(98-digit number)
64241277581007003808…00818967268683292799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.424 Γ— 10⁹⁷(98-digit number)
64241277581007003808…00818967268683292801
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
1.284 Γ— 10⁹⁸(99-digit number)
12848255516201400761…01637934537366585599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.284 Γ— 10⁹⁸(99-digit number)
12848255516201400761…01637934537366585601
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:57,938,302 XPMΒ·at block #6,836,751 Β· updates every 60s
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