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Block #356,530

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/12/2014, 7:39:13 PM Β· Difficulty 10.3791 Β· 6,438,900 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
180769be7f3f9a744eaf949347298d1a06b535dbceaf09c71df7dd4aa5e76f95
View on Chainz β†—

Height

#356,530

Difficulty

10.379148

Transactions

2

Size

391 B

Version

2

Bits

0a610fd5

Nonce

1,489

Timestamp

1/12/2014, 7:39:13 PM

Confirmations

6,438,900

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c6b8581d402a2bc82f56a792eab5ea3bf697a4e364981b68ac52f681b2387499
Transactions (2)
Coinbase3eae21e8323789…52ec3a87f88e45
1 in β†’ 1 out9.2800 XPM110 B
AeKNrjNj…1NEq95Ta
75177074d8b671…22cf7e6c4e800f
1 in β†’ 1 out3.0596 XPM191 B
AVgjJjaQ…W9g78ULh
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.

3.018 Γ— 10⁹⁡(96-digit number)
30183975688124180853…16276107929617092299
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
3.018 Γ— 10⁹⁡(96-digit number)
30183975688124180853…16276107929617092299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.018 Γ— 10⁹⁡(96-digit number)
30183975688124180853…16276107929617092301
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
6.036 Γ— 10⁹⁡(96-digit number)
60367951376248361706…32552215859234184599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.036 Γ— 10⁹⁡(96-digit number)
60367951376248361706…32552215859234184601
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
1.207 Γ— 10⁹⁢(97-digit number)
12073590275249672341…65104431718468369199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.207 Γ— 10⁹⁢(97-digit number)
12073590275249672341…65104431718468369201
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
2.414 Γ— 10⁹⁢(97-digit number)
24147180550499344682…30208863436936738399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.414 Γ— 10⁹⁢(97-digit number)
24147180550499344682…30208863436936738401
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
4.829 Γ— 10⁹⁢(97-digit number)
48294361100998689365…60417726873873476799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.829 Γ— 10⁹⁢(97-digit number)
48294361100998689365…60417726873873476801
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:57,607,503 XPMΒ·at block #6,795,429 Β· updates every 60s
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