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Block #314,879

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2013, 5:15:19 AM Β· Difficulty 10.0783 Β· 6,499,003 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52603882f5f18f04b1e2431f06d82e00fbe1ff4677997a33028869896a0ac92c
View on Chainz β†—

Height

#314,879

Difficulty

10.078340

Transactions

1

Size

1.11 KB

Version

2

Bits

0a140e1b

Nonce

395,512

Timestamp

12/16/2013, 5:15:19 AM

Confirmations

6,499,003

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

c92a6afa088e220b9a29c00dd8eae7a788d582507ca15a7ccc2cf908171bab32
Transactions (1)
Coinbasec92a6afa088e22…2cf908171bab32
1 in β†’ 29 out9.8100 XPM1.02 KB
Aac9Hjdg…P4ktypc3ANNg88pG…ppn21sTeASFLBMf4…aN3am9vAAe58nAEb…GFUA15fvAc8Wh9TD…3kJsjtfo
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.

5.819 Γ— 10⁹⁴(95-digit number)
58194897785861534417…21752115271613095759
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
5.819 Γ— 10⁹⁴(95-digit number)
58194897785861534417…21752115271613095759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.819 Γ— 10⁹⁴(95-digit number)
58194897785861534417…21752115271613095761
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
1.163 Γ— 10⁹⁡(96-digit number)
11638979557172306883…43504230543226191519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.163 Γ— 10⁹⁡(96-digit number)
11638979557172306883…43504230543226191521
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
2.327 Γ— 10⁹⁡(96-digit number)
23277959114344613767…87008461086452383039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.327 Γ— 10⁹⁡(96-digit number)
23277959114344613767…87008461086452383041
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
4.655 Γ— 10⁹⁡(96-digit number)
46555918228689227534…74016922172904766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.655 Γ— 10⁹⁡(96-digit number)
46555918228689227534…74016922172904766081
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
9.311 Γ— 10⁹⁡(96-digit number)
93111836457378455068…48033844345809532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.311 Γ— 10⁹⁡(96-digit number)
93111836457378455068…48033844345809532161
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:57,755,131 XPMΒ·at block #6,813,881 Β· updates every 60s
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